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Bopt.  Mocli,  Bng. 


Dopt.  Mooh.  ESng. 


THE 


Dopt.Moobi.Bng. 
GALVANOMETER, 

AND    ITS    USES. 

A  MANUAL  FOR 

ELECTRICIANS    AND    STUDENTS. 

BY 

C.    H.    HASKINS. 
THIRD  EDITION. 

WITH  ILLUSTRATIONS. 

NEW    YORK: 

D.    VAN    NOSTRAND,    PUBLISHER, 

23  MURRAY  ST.  AND  27  WARREN  ST. 

1884. 


Entered  according  to  Act  c'  Congress,  in  the  year  1881,  by 

D.  VAN    NOSTRAND, 
In  the  Office  of  the  Librarian  of  Congress,  at  Washington. 


Electrotyped  by  SMITH  &  McDoucAL,  82  Beekman  St. 


Dopt.  Mooh. 


PREFACE. 


r~PHE  author  has  endeavored  to  present  within  the 
limits  of  this  little  volume,  in  a  condensed 
form,  a  statement  of  electrical  laws  and  rules  for 
measurement,  written  in  a  plain,  brief  manner,  to- 
gether with  such  tables  and  simple  formulae  as  will 
enable  any  student,  with  a  little  practice,  to  make 
land  line  measurements  with  dispatch  and  accu- 
racy. 

He  trusts,  also,  that  it  will  be  valuable  to  his 
more  experienced  brethren  as  a  book  of  reference, 
obviating  the  necessity  of  search  through  the  works 
of  different  authors  for  what  will  here  be  found  in  a 
condensed  and  convenient  form. 

Considerable  matter  relative  to  construction  and 
maintenance  of  lines,  care  of  battery,  etc.,  which  the 
author  had  prepared,  has  been  omitted  in  order  that 
the  book  might  be  confined  to  the  original  plan — that 
of  a  manual  of  measurement. 

The  author  has  no  apologies  to  make  for  any  errors 
of  omission  or  commission.  If  this  effort  should 


iv  PREFACE. 


stimulate  another  to  the  preparation  of  a  more  com- 
plete work,  the  profession  will  be  benefited  thereby, 
and  the  author  fully  compensated  for  his  labors. 

To  the  gentlemen  who  have  furnished  formulae,  and 
especially  to  his  friend  F.  L.  POPE,  the  author  returns 
his  sincere  thanks. 


CONTENTS. 


EXPLANATORY     CHAPTER. 

PAGE 

Resistance  of  Conductors 7 

Units  of  Measurement 8 

Electromotive  Force 8 

Quantity 9 

Cause  of  the  Flow  of  the  Current 9 

Law  Regulating  the  Flow  of  the  Current 10 

Quantity  and  Tension  of  Batteries 10 

Proportioning  Battery  to  Line 12 

The  Speed  of  the  Current 15 

Effect  of  Atmospheric  Moisture  on  Insulation 17 

Joint  Resistance  of  Lines 18 

Galvanometers 19 

Rheostats 20 

Shunts 20 


CHAPTER     II. 

Tangent  Galvanometer 21 

Connections  for  Measurement 23 

Testing  for  Insulation 24 

Gaugain  Galvanometer 25 

Differential  Galvanometer 26 

Wheatstone  Bridge 27 

Sine  Galvanometer 32 


vi  CONTENTS.  • 


CHAPTER     III. 

Formulae  to  measure  Electromotive  Force  and  Internal  ?A 

Resistance  of  a  Battery 

By  method  of  Equal  Deflections.. . 


By  Direct  Measurement 

Internal  Resistance  of  Battery 

Mance's  Formulae 3 . 

Measurement  of  Electromotive  Force  by  Comparison  36 

Measurement  of  Insulation 36 

Testing  for  Conductivity 38 

Line  Resistance  measured  from  an  Intermediate  Sta- 
tion   38 

Corrected  Line  Resistance,  by  Schwendler 39 

Testing  for  Grounds 40 

By  Loop  Test 4I 

Testing  for  Crosses 42 

Testing  Bad  Grounds 45 

Shunts 45 

Units  of  Measurement 6 


Weight  of  Insulated  Office  Wire 47 

Specific  Resistance  of  Different  Metals 47 

Table  of  Weight  and  Resistance  of  Copper  Wires 48 

Electromotive  Force  of  Batteries 49 

Table  of  Natural  Tangents 50 

English  and  French  Measure 53 

Table  of  Sines  and  Tangents 54 

Table  of  the  Sizes,  Weights,  Resistances,  and  Breaking 

Strain  of  Iron  Wires: 56 

Table  of  Squares,  Cubes,  Square  and  Cube  Roots 57 


APPENDIX 77 


J 


EXPLANATORY   CHAPTER. 

To  enable  the  student  to  work  understanding^  in 
salvanometric  measurements,  it  is  necessary  that 
Should  comprehend  the  laws  upon  which  such 
urements  are  based. 

These  laws  we  will  state,  in  as  few  and  simple  words 
as  possible ;  and  the  student,  if  he  masters  them  thor- 
oughly, will  be  enabled  to  understand  readily  what 

^Resistance  of  Conductors. -All  conductors 
offer  a  certain  degree  of  resistance  to  the  passage  o 
the   electric   current   through   their   substance 
resistance  varies  with  different  materials.     The  follow- 
ing table  illustrates  the  comparative  resistances  of  the 
most  common  metals  to  the  passage  of  the  current, 
;ilver   being  taken   as   the   standard.     The   measure 
ments  are  taken  at  32°  Fahrenheit. 


Silver,  hard 100 

Copper,  hard 100 

Gold,  hard 128 

Iron 594 

Tin 8°9 


Lead i 

Brass 45° 

German  Silver '1282 

Platinum  and  silver..  1493 
Mercury 58l5 

Jenkin. 


The  resistance  of  metals  increases  with  their  tner 
mometric  heat.  For  instance,  iron  wire  increases  abou 
35  per  cent,  for  each  degree  Fahrenheit  above  60  . 

The  conductivity  (which  is  the  reverse  of  resistance 
of  soft  iron  wire,  suitable  for  telegraph  purposes,  i 
about  \  that  of  commercial  copper  wire. 

The  conductivity  of  any  wire  increases  as  its  weigh 

per  foot.  . 

The  resistance  of  any  iron  wire,  per  mile,  is  loun 
by  dividing  360,000  by  the  square  of  its  diameter,  Th 


8  MEASUREMENT — FORCE. 


quotient  will  be  in  ohms  at  60°  Fahrenheit.    This  is 

^60  ooo 
expressed  thus          ' — ,    d  being  the  diameter  of  the 

wire.     Or  it  may  be  measured,  as  hereafter  explained. 

Knowing,  then,  the  resistance,  per  mile,  that  a  given 
wire  offers,  or  should  offer,  to  the  passage  of  a  current, 
we  have  a  basis  for  comparison,  and  can  readily  ascer- 
tain its  electrical  condition,  and,  when  defective,  apply 
a  remedy  where  and  when  required. 

2.  Units  of  Measurement. — To  determine  accu- 
rately the  amount  or  degree  of  resistance,  we  must 
have  some  standard  that  will  serve  us  as  the  inch  does 
in  the  measurement  of  distance,  or  a  grain  in  estimating 
weight.     Several  of  these  standards  have  been  made. 
(See  Table  of  Units  of  Resistance^) 

But  two  standards,  however,  are  now  in  general  use, 
and  these  two  only  shall  we  note  here. 

The  Ohm  is  the  standard  unit,  adopted  by  the  British 
Association,  and  in  general  use  in  this  country.  It  is 
equal  to  the  resistance  of  a  prism  of  pure  mercury  of 
i  square  millimetre  section  and  1.0486  metres  length, 
at  32°  F. 

The  Siemens  Unit  is  equal  to  the  resistance  of  a 
prism  of  pure  mercury  of  i  square  millimetre  section, 
and  i  metre  long,  at  32°  F.  The  Siemens  Unit  is  in 
general  use  on  the  European  continent,  and  to  a  con- 
siderable degree  in  the  United  States. 

To  convert  Siemens  into  Ohms,  multiply  by  the 
decimal  .9536. 

To  convert  Ohms  into  Siemens,  multiply  by  1.0486. 

Having  found  our  units  of  measurement,  we  will 
now  consider  the  laws  governing  the  flow  of  the 
current.* 

3.  Electromotive  Force. — The  power  which  a  cell 
of  battery  possesses  of  causing  the  transfer  of  its  cur- 

*  In  examples  given  in  this  work,  the  term  u  unit"  is  used  as  a  "unit 
of  measurement,"  and  may  be  read  either  as  an  Ohm  or  Siemens'  unit. 
When  absolute  measurements  are  given,  the  word  Ohm  or  Siemens  is 
always  given  to  distinguish  the  kind  of  unit  meant. 


QUANTITY— THE  FLOW  OF  THE  CURRENT. 


rent  from  one  place  to  another  is  its  electromotive 
force.  In  other  words,  the  electromotive  force  of  a 
current  is  its  power  of  overcoming  resistance  —  its 
energy.  To  use  a  familiar  comparison,  electromotive 
force  is  to  a  current  what  pressure  is  to  steam. 

4.  Quantity. — The  amount  of  current  that  is  evolved 
in  a  given  time  by  a  cell  of  battery  is  termed  its  quan- 
tity.    This  amount  may  be  increased  or  diminished  by 
lessening  or  increasing  the  resistance  in  circuit  both 
in  the  battery  and  external  thereto. 

5.  Cause  of  the  Flow  of  the  Current. — While 
chemical  action  is  going  on  in  a  battery,  the  current  is 
being  constantly  accumulated,  or  piled  up,  at  the  posi- 
tive pole  of  the  battery,  with  a  vigor  depending  en- 
tirely upon  the  electromotive  force  of  the  battery. 

The  old  theory,  that  the  current  thus  accumulated 
flowed  along  the  line  wire  to  the  ground  at  the  dis- 
tant end,  and  back  to  the  other  terminal  of  the  battery 
through  the  ground,  is  now  generally  abandoned,  and 
the  theory  of  M.  Gavarret  accepted  as  correct. 

He  teaches  that  the  earth  being  a  common  recep- 
tacle and  reservoir  of  electricity — hence  termed  the 
"common  reservoir" — has  no  electrical  tension. 

When  the  current  in  a  battery  accumulates  at  the 
positive  pole  of  the  battery,  its  tension  is  greater  than 
that  of  the  earth.  Now  connect  a  wire  from  each  end 
of  the  battery  to  the  ground.  If  these  wires  are  short 
and  thick,  thus  having  practically  no  resistance,  the 
current  will  flow  from  the  positive  pole  of  the  battery 
through  the  wire  to  the  earth  with  a  degree  of  energy 
depending  upon  its  excess  of  tension  over  that  of  the 
earth.  This  action  will  continue,  the  earth  receiving 
and  absorbing  from  the  positive  pole  of  the  battery 
where  the  tension  is  greater,  and  giving  to  the  nega- 
tive pole  where  the  tension  is  less,  until  the  action  of 
the  battery  ceases  from  exhaustion,  and  the  tension  of 
the  battery  and  the  earth  are  equal. 

The  effort,  then,  of  the  current  evolved  by  the  bat- 


io    FLOW  OF  CURRENT — QUANTITY  OF  BATTERIES. 


tery,  is  to  equalize  the  tension  or  pressure,  and  produce 
an  electrical  equilibrium.  This  same  inequality  of  ten- 
sion between  the  clouds  and  the  earth,  is  the  cause  of 
lightning-storms. 

6.  L,aw  regulating  the  Flow  of  the  Current.  — 

If,  in  the  case  above  supposed,  the  wires  connecting 
i  the  battery  with  the  earth,  were  so  long,  or  so  thin,  as 
to  interpose  considerable  resistance  to  the  passage  of 
the  current,  the  flow  would  be  less  in  amount,  and  the 
chemical  action  of  the  battery  less  rapid  —  the  current 
being  dammed,  or  choked  back,  by  the  resistance  to 
its  passage, 

The  amount  of  current,  then,  that  will  flow  to  line, 
depends  upon  and  is  proportionate  to  the  resistance 
of  the  circuit,  Hence  Ohms  law,  which  is  the  founda- 
tion of  all  electrical  measurements. 

Ohms  law  is  stated  thus  : 

C  being  the  amount  of  current, 
E  the  electromotive  force,  and 
R  the  resistance  in  the  circuit. 


or,  the  current  flowing  to  line,  equals  the  electromotive 
force  divided  by  the  resistance. 

7.  Quantity  and  Tension   of  Batteries.  —  The 

amount  of  current  generated  by  a  cell  of  battery  de- 
pends upon  the  size  of  its  plates  —  the  tension,  upon 
the  number  of  cells. 

Hence,  a  battery  of  forty  cells,  while  giving  forty 
times  the  electromotive  force,  or  tension*  of  one  cell,  will 
furnish  only  the  same  amount  or  quantity  of  current. 
Each  cup  of  battery  has  its  own  quantity,  which  is 
urged  forward  to  the  next  cell,  by  virtue  of  its  own 

*  Electro-motive  force  may  be  defined  as  tension  in  a  state  of  motion;  and 
tension,  as  electromotive  force  in  a  state  virest, 


QUANTITY  AND  TENSION  OF  BATTERIES.         11 


electromotive  force.  The  current  from  the  cell  at  the 
positive  pole  of  the  battery,  is  pushed  out  to  the  line- 
wire,  the  current  from  the  next  cell  taking  its  place  — 
the  last  cell  being  supplied,  through  the  ground-wire, 
from  the  earth.  But  the  current  from  each  cell,  when 
carried  forward  to  its  neighbor,  parts  with  its  energy 
or  electromotive  force  ;  and  the  current  from  the  first 
cell  is  pushed  forward  to  line,  and  thence  to  the  ground 
at  the  further  end  of  the  line,  with  all  the  electromo- 
tive force,  or  energy,  of  all  the  cells. 

The  amount  of  current  flowing  to  line,  from  a  given 
battery,  is  regulated,  as  we  have  seen,  by  the  resistance 
of  the  circuit  —  and  in  this  must  be  included  the  inter- 
nal resistance  of  each  cell  of  the  battery.  But,  with  a 
given  total  resistance,  the  flow  of  current  may  be  in- 
creased : 

i  st.  By  increasing  the  size  of  the  cells,  and  thus  de- 
creasing the  total  resistance  in  the  circuit  ;  and, 

2d.   By  adding  more  cells. 

If  we  consider  only  the  internal  resistance  of  the 
cells,  the  addition  of  more  cells  will  not  increase  the 
current. 

Thus,  if  we  have  i  cell  of  battery,  with  an  internal 
resistance  of  2  units,  and  an  electromotive  force  of, 
say,  10,  and  the  poles  connected  by  a  wire  having 
practically  no  resistance,  the  proportion  of  current 
flowing  to  line  will  be  5  . 


Now  take  5  cells, 

E  —  5  x  10  =  50  _ 
~R—  5  x  2  =  10  ~~  •>  * 

The  product  is  still  5,  because  the  divisor  and  divi- 
dend are  both  changed  in  the  same  ratio. 


12  PROPORTIONING  BATTERY  TO  LINE. 


But  suppose  the  resistance  of  the   line-wire  to   be 
5  units,  represented  by  r.    Then  with  i  cell  we  have, 


,  =  IO 

-=='43. 


and  with  5  cells, 


or  nearly  three  times  as  much  current  as  before. 

8.  Proportioning  Battery  to  Line.— It  will  be 
seen,  therefore,  that  the  proper  method  for  adapting  a 
battery  to  any  line,  with  any  instruments,  is  to  select 
a  form  of  battery  giving  sufficient  current  to  saturate 
the  magnets  of  the  relays  to  their  maximum,  and  then 
add  a  sufficient  number  of  cells,  to  drive  it  with  the 
necessary  force  to  produce  the  desired  effect. 

The  sum  of  the  resistances  of  all  the  instruments  in 
a  circuit,  should,  as  nearly  as  practicable,  balance  the 
resistance  of  the  line-wire.  In  no  case  should  they  ex- 
ceed the  wire  resistance. 

"  IV hen  the  resistance  of  the  coils  of  the  electro-magnet 
is  equal  to  the  resistance  of  the  rest  of  the  circuit,  i.  e.,  the 
conducting  wire  and  battery,  the  magnetic  force  is  a  max- 
imum"— (NOAD's  Text  Book.) 

"The  application  of  this  law  to  a  telegraphic  circuit 
would  be  to  make  the  sum  of  the  resistances  of  all  the 
magnet-coils  in  circuit,  equal  to  the  resistance  of  the 
line  and  batteries  ;  but  as  in  practice  the  resistance  of 
a  telegraphic  circuit  varies,  being  considerably  reduced 
by  defective  insulation,  the  total  resistance  of  the  in- 
struments should  be  less  than  that  of  the  line  when  in 
good  condition,  to  attain  the  best  results  during  unfa- 
vorable weather." — (POPE'S  Modern  Practice,  page  152.) 

A  safe,  practical  rule  for  determining  the  number  of 
cups  of  main  battery  needed,  is  to  call  the  resistance 
of  the  relays  equal  to  the  line-wire,  and  use  one  cup  of 
Grove,  or  bichromate  of  potash  (electropoion),  or  two 


PROPORTIONING  BATTERY  TO  LINE.  13 


cells  of  Calland  or  Hill  battery  to  each  100  units  re- 
sistance in  the  circuit. 

Thus,  for  example  :  suppose  a  circuit  of  200  miles 
No.  9  wire. 

This  will  measure  20  units  to  the  mile,  or  .  .4000  units. 
8  relays  in  circuit,  500  units  each 4000     " 

Total  resistance 8000    " 

For  Grove  or  bichromate,  divide  by  100,  and  we  get 
80  cups  battery,  40  at  each  terminal  of  the  wire.  For 
sulphate  copper  battery,  divide  by  50,  and  we  find  that 
we  need  160  cups  of  battery,  80  at  each  end. 

These  figures  are  true  only  of  single  wires.  When 
several  wires  are  worked  from  one  battery,  the  total 
amount  of  battery  used  is  of  course  much  less.  The 
number  of  lines — of  about  equal  resistance — that  may 
be  worked  from  the  same  battery  varies  greatly  with 
different  batteries,  depending  upon  the  chemical  en- 
ergy of  the  battery,  the  quantity  of  current  evolved  by 
it,  and  its  liability  to  polarization. 

Thus,  the  bichromate  batteries  of  80  cups,  that  we 
determined  upon  for  our  8000  unit  line,  will  furnish 
current  enough  for  several  lines  of  the  same  resistance. 
But  as  we  add  wires  we  lessen  the  external  resistance, 
until,  owing  to  the  slight  resistance,  the  action  is  so 
rapid  that  the  battery  polarizes  and  action  ceases. 
Practically,  not  over  six  to  eight  lines  can  be  worked 
from  this  battery. 

With  Grove  it  is  different.  Lines  may  be  added  to 
a  Grove  battery,  with  perfect  safety,  up  to  forty  or 
fifty. 

The  sulphate  copper  batteries  have  too  much  inter- 
nal resistance  to  allow  the  addition  of  many  wires. 
Three  lines  are  worked  from  sulphate  copper  batteries 
having  jars  six  inches  in  diameter. 

In  all  cases,  the  expenditure  or  consumption  of  ma- 
terial in  a  battery  is  in  exact  proportion  to  the  work 


PROPORTIONING  BATTERY  TO  LINE. 


done  ;  that  is,  to  the  current  evolved.  Therefore,  the 
expenditure  of  battery  material,  with  three  lines  to  a 
battery,  is  three  times  that  of  one  line  to  the  same 
battery,  and  there  is  no  economy  in  working  several 
lines  from  one  battery,  except  in  room  occupied. 

The  disadvantage  of  working  several  lines  from  one 
battery  is  the  interference  of  the  circuits  with  each  other 
in  bad  weather.  Sometimes  this  interference  is  quite 
serious.  A  greater  number  of  cells  of  battery  than  is 
absolutely  needed  to  work  the  circuit  promptly,  is  in- 
jurious, and  in  wet  weather  it  tends  to  make  the  line 
work  badly.  Indeed,  the  effect  of  an  excess  of  battery 
is  often  as  detrimental  to  a  line,  in  wet  weather,  as  bad 
insulation,  or  a  conducting  wire  of  too  high  resistance. 

To  explain  this,  the  reader  will  remember  that  the 
difference  in  resistance  between  the  line-wire  and  the 
insulators,  is  the  margin  upon  which  the  line  is  worked. 
If  that  margin  is  diminished  by  bad  insulation,  a  por- 
tion of  the  current  escapes  to  the  ground.  If  the  re- 
sistance of  the  line-wire  is  increased,  the  margin  is 
again  diminished,  and  a  portion  of  the  current  escapes 
as  before. 

Now,  the  higher  the  tension  of  the  battery-current, 
the  more  readily  will  it  escape  from  the  line,  because 
the  greater  is  its  power  to  overcome  resistance.  The 
effect,  then,  upon  a  wet  day,  is  the  same,  upon  the 
line,  whether  the  insulation  is  defective,  or  the  battery 
too  large.* 

Thus  it  will  be  seen  that  adding  more  battery  to  a 
heavy-working  line,  will  often,  in  wet  weather,  make  it 
work  worse  than  before.  And  it  will  also  be  noted, 
that  relays  of  high  resistance,  as  they  add  to  the  resist- 
ance of  the  line-wire,  decrease  the  working  margin 


*  If,  however,  the  escape  is  not  very  serious,  it  is  sometimes  beneficial 
to  add  battery  to  sending  end  until  you  have  so  high  a  current  that,  in 
addition  to  the  large  amount  escaping,  enough  will  reach  the  further  end 
to  work  the  relay.  In  this  case  the  receiver  must  not  attempt  to 
11  break." 


J 


THE  SPEED  OF  THE  CURRENT. 


between  the  line   and  insulator  resistance,  and  thus 
increase  the  tendency  of  the  current  to  escape. 

When  the  relays  of  a  line,  of  say  200  miles,  are  pro- 
portioned to  the  line  itself,  that  is,  do  not  exceed  the 
line-wire  resistance,  and  the  battery  is  adapted  to  the 
circuit  by  the  rule  above  given,  if  the  line  is  well  insu- 
lated, it  will  work  well,  in  very  bad  weather,  when  a 
similar  line,  equipped  with  high  resistance  relays,  or  an 
excess  of  battery,  will  scarcely  work  at  all.* 

9.  The  Speed  of  the  Current. — Many  experi- 
ments have  been  made  to  determine  the  speed  of  trans- 
mission of  the  electric  current  or  influence  through 
a  wire.  The  first  measurement,  made  by  Wheatstone 
in  1833,  showing  a  speed  of  288,000  miles  per  second, 
was  taken  as  the  speed  of  the  current  under  all  circum- 
stances. Subsequent  measurements,  however,  showed 
such  variable  results,  that  confidence  in  Wheatstone's 
figures  was  much  shaken.  The  following  table  shows 
the  rates  of  speed  noted  by  various  experimenters  : 


Date. 

Length  of 
Circuit. 

Velocity 
Per 
Second. 

Observer. 

Remarks. 

1833 

.5  mile 

288,000 

Wheatstone 

Leyden  Jar. 

1849 

880 

18,700 

Walker 

Relay. 

k 

59«> 

16,000 

u 

u 

4 

607 

28,500 

Mitchell 

u 

1850 

260  iron 

60,000 

Fizeau  &  Gounelle 

Galvanometer  needle. 

1 

130  copper 

114,000 

41                                 U 

U                                  U 

' 

1045 

15,000 

Gould 

Relay. 

1 

447 

17,000 

Walker 

" 

1854 

230 
104  iron 

13,000 
115,000 

Guilleman  &  Burnouf 

Chemical  Telegraph. 
Galvanometer  needle. 

*  A  line  that  is  suffering  from  bad  escape  may  be  worked  much  better 
for  through  business  in  bad  weather,  by  switching  off  the  battery  at  the 
receiving  end  of  the  line,  and  receiving  only  by  the  sending  office  cur- 
rent. Because,  if  there  are  heavy  escapes  on  the  line,  the  sending  opera- 
tor does  not  break  all  the  current  from  the  battery  at  the  receiving  end  of 
the  line,  thus  leaving  the  receiving  relay  partially  magnetized  constantly, 
and  consequently  less  sensitive  to  the  small  portion  of  current  from  the 
sender  that  reaches  the  receiving  station.  Whereas,  if  the  only  current 
on  the  wire  is  that  of  the  sender,  the  portion  of  his  current  that  does 
reach  the  other  end  of  the  line  comes  clear  and  sharp. 


16  THE  SPEED  OF  THE  CURRENT. 


The  above  table  gives  no  data  from  which  to  make 
any  calculation  or  deduce  any  law.  It  only  serves  to 
show  how  varied  were  the  results  obtained.  To  be  of 
any  benefit,  the  experimenters  should  have  given  the 
conductivity,  per  mile,  of  the  wire  used,  the  form  of 
battery,  and  the  number  of  cells  used  in  each  case. 
The  English,  French,  and  German  experimenters  use, 
also,  miles  of  different  lengths. 

Thus,  for  land  lines,  we  were  without  any  reliable 
data  until  1869,  when  Prof.  G.  W.  Hough,  of  Dudley 
Observatory,  and  Mr.  C.  S.  Jones,  of  Albany,  New 
York,  undertook  a  series  of  experiments  to  determine 
the  velocity  of  the  current.  Mr.  Jones,  manager  of  the 
Western  Union  office,  by  looping  wires  to  Boston,  De- 
troit, New  York,  and  Buffalo,  obtained  circuits  of  suffi- 
cient length  to  test  the  question  thoroughly. 

As  Grove  battery  was  used,  and  the  line-wire  was 
galvanized  No.  9,  we  have  some  data  from  which  to 
draw  satisfactory  conclusions. 

On  the  27th  of  May,  Messrs.  Hough  and  Jones  ob- 
tained the  following  results : 


Velocity  per  Second. 

No.  Cells  of  Battery. 

Length  of  Circuit. 

10,200  miles. 
20,000    u 
29,450    " 
18,200 

r 

160 
295 

295 

400  miles. 
400     l 
400     l 

IOOO 

Prof.  Hough  remarks,  in  relation  to  the  above  re- 
sults : 

"  An  inspection  of  these  results  show  at  a  glance, 
that  the  velocity  increases  with  the  number  of  battery 
elements  employed ;  also,  for  the  same  battery  it  de- 
creases with  the  length  of  the  circuit." 

From  these  figures  we  deduce  these  facts : 

First. — That  with  a  given  resistance,  the  speed  in- 
creases with  the  increase  of  the  electromotive  force, 


EFFECT  OF  MOISTURE  ON  INSULATION.  17 


i.  e.,  the  power  to  overcome  resistance  and  urge  the 
current  forward. 

Second. — That  with  a  given  battery,  the  speed  of  the 
current  varies  as  the  resistance  to  be  overcome  in  the 
circuit  varies. 

And  these  facts  explain  why  Wheatstone  obtained  a 
velocity  of  288,000  miles  per  second,  when  Hough  and 
Jones  show  less  than  30,000  miles  as  their  greatest  ve- 
locity. Wheatstone  used  a  Leyden  jar,  discharging  a 
current  therefrom  of  the  highest  tension,  and  having 
but  a  half  mile  of  resistance  of  circuit,  while  the  Albany 
experiments  were  made  through  long  circuits,  with 
battery-currents  of  comparatively  very  low  tension. 

IO.  Effect  of  At mosplieric  Moisture  on  Insula- 
tion.— The  effect  of  a  moist  or  dry  atmosphere  on  line 
measurements  is  too  generally  overlooked,  especially 
on  lines  insulated  with  glass.  As  an  insulator,  glass  is 
probably  the  best  in  dry  weather,  as  it  is  certainly  one 
of  the  worst  when  surrounded  by  a  saturated  atmos- 
phere. Being-  an  excellent  radiator  of  heat,  the  glass 
insulator  readily  gives  it  out  to  the  passing  breeze,  and 
speedily  becomes  cold,  when  the  particles  of  moisture 
held  in  suspension  in  the  air  are  deposited  in  a  con- 
densed form  on  the  surface  of  the  glass,  thus  forming 
a  film  of  water,  through  which  the  current  escapes. 

Again,  even  with  the  most  perfect  insulation,  with  a 
saturated  atmosphere,  a  line  will  show  considerable 
general  escape.  Frequently,  a  lower  degree  of  insula- 
tion is  shown  just  before  a  heavy  rain  than  after  it  be- 
gins falling.  And  although  the  most  careful  experi- 
ments fail  to  show  any  escape  through  the  atmosphere 
from  one  particle  of  moisture  to  another,  yet  this  heavy 
escape  is  often  noted,  as  above  stated.  When  the  rain 
begins  falling,  the  moisture  being  condensed  into  drops, 
the  continuity  of  the  moisture  seems  destroyed,  and  the 
escape  consequently  checked. 

Whenever  practicable,  then,  the  percentage  of  sat- 


i8  JOINT  RESISTANCE  OF  LINES. 


uration  of  the  atmosphere,  shown  by  a  hygrometer, 
should  be  recorded,  with  the  measurement,  for  future 
use,  in  comparing  the  condition  of  a  line  at  different 
times. 

11.  Joint  Resistance  of  Lines. — By  attaching  a 
second  wire  to  a  battery,  a  second  path  is  provided  for 
the  current,  and  the  resistance  to  its  flow  therefore 
lessened.  If  both  wires  are  of  exactly  the  same  resist- 
ance, the  effect  is  the  same  as  if  the  first  wire  were 
taken  off  and  replaced  with  one  of  just  double  the  ca- 
pacity, or  weight  per  foot,  or  one  of  half  its  length  of 
the  same  capacity. 

The  joint  resistance — that  is,  the  resistance  of  all  the 
wires  attached  to  a  battery — to  the  flow  of  its  current, 
may  be  found  as  follows  : 

If  the  resistance  of  the  wires  is  equal,  the  sum  of  the 
resistances,  divided  by  the  square  of  their  number,  or  the 
resistance  of  one  wire,  divided  by  the  number  of  wires, 
will  give  the  joint  resistance. 

Thus,  four  wires  of  100  ohms  each  : 

ist  method, 
2d  method, 


4??  =  25  ohms. 
16 


I??  =  25  ohms. 
4 

When  the  resistance  of  two  wires  is  unequal,  the 
resistance  may  be  found  by  dividing  their  product  by 
their  sum. 

Suppose  two  wires  of  200  and  300  ohms  resistance, 

200  x  300  =  60,000  =I2QQhms> 
200  -f  300  =     500 

When  more  than  two  wires,  find  the  joint  resistance 
of  the  first  two,  as  above  ;  then  take  the  result,  consid- 
ering it  as  a  single  wire,  and  proceed  in  the  same 
manner. 


GALVANOMETERS.  19 


Suppose  we  have  three  wires,  of  200,  300,  and  280 
ohms.  The  joint  resistance  of  the  first  and  second  is, 
as  we  have  seen,  120  ohms. 

120  x  280      33,600      0       , 

=  — —  84  ohms, 

1 20  +  280         400 

the  joint  resistance  of  the  three  wires. 

Or,  it  may  be  obtained  by  the  following  formula : 

i st.  Calling  the  three  wires  a,  b,  c, 

abc 
ab  -f  ac  +  be ' 

200  x  300  x  280 

—  =  84  ohms. 


200  x  300  +  200  x  280  +  300  x  280 

2d.  Divide  one  by  the  sum  of  the  reciprocals*  of 
their  several  resistances. 

i 


The  reciprocal  of  200  is  .................  005 

"   300  is  .................  00333  + 

"  "          "   280  is  .................  00357  + 


.01190 
and, 

=  84  ohms. 


.01190 

12.  Galvanometers. — A  magnetic  needle  will  be 
deflected  from  the  north  by  a  current  of  electricity 
flowing  in  a  conductor  placed  parallel  to  it.  If  the 
conductor  is  placed  on  top  of  the  needle,  and  parallel, 
when  the  positive  pole  of  the  battery  is  attached  to  the 
south  end  of  the  conductor,  and  its  negative  end  to  the 

*  The  reciprocal  of  a  number  is  the  quotient  of  i  divided  by  that 
number.  Thus  the  reciprocal  of  2,  is  —  ;  of  20,  is  -^-  , 


20  RHEOSTATS — SHUNTS. 


north  end,  the  current  will  flow  northward,  and  the 
north  end  of  the  needle  will  be  deflected  to  the  left. 
Reverse  the  current,  and  the  north  end  will  be  deflect- 
ed to  the  right.  If  the  conductor  is  placed  under  the 
needle,  the  action  will  be  in'the  reverse  direction. 

The  degree  of  deflection  will  be  proportional  to  the 
strength  of  the  current. 

If  the  conductor  is  carried  over  the  face  of  the  needle, 
and  back  underneath,  the  effect  will  be  doubled.  Wind 
the  wire  in  several  convolutions  parallel  to  the  needle, 
making  a  helix,  with  the  needle  in  the  centre,  and  you 
have  the  strongest  form  of  galvanometer.  The  finer 
the  wire,  and  the  greater  the  number  of  convolutions, 
the  more  sensitive  will  the  needle  be  to  the  current 
passing  through  the  wire  of  the  helix. 

13.  Rheostats. — By  using  fine   German-silver  or 
silver  and  platinum  wire,  the  resistance  of  which  is 
not  affected  by  changes  of  temperature,  we  may  make 
a  series  of  coils  whose  resistance  is  equivalent  to  that 
of  any  number  of  miles,  or  fractions  of  miles.     A  num- 
ber of  these  coils,  arranged  to  be  thrown  in  and  out  of 
circuit  at  pleasure,  is  termed  a  Rheostat. 

14.  Shunts. — It  is  sometimes  necessary,  in  meas- 
urements, to  divert  a  portion  of  the  current  from  a 
galvanometer,  to  reduce  the  deflection  of  the  needle 
within  proper  limits.     In  this  case,  a  wire  or  coil  of 
greater  or  less  resistance  is  used,  which  is  connected 
to  both  posts  of  the  instrument  to  be  shunted.     The 
current  will  then  divide  inversely  as  the  resistance  of 
the  two  paths  or  routes  open  to  it.     Suppose  a  galvan- 
ometer coil  to  have  a  resistance  of  99  ohms,  and  the 
shunt-wire  of  i  ohm.     Then  -ffo  of  the  current  would 
pass  through   the  shunt  wire,    and  Tfg-  through  the 
galvanometer. 

In  this  case,  the  result  shown  by  the  galvanometer 
must  be  multiplied  by  the  shunt  to  obtain  the  correct 
answer.  See  rules  for  making  shunts. 


TANGENT  GALVANOMETER.  21 


CHAPTER    II. 

1.  Tangent  Galvanometer. — "The  intensity  of 
the  current,  as  measured  by  the  tangent  galvanometer, 
is  proportioned  to  the  tangent  of  angle  of  deflection  " 
of  the  needle. 

"  Bradley 's  Improved  Tangent  Galvanometer,"  is 
the  only  one  in  use  in  the  United  States  for  line  work, 
and  is  undoubtedly  the  most  accurate  tangent  instru- 
ment made.  We  quote  the  description  from  Dr.  Brad- 
ley's  pamphlet.  The  needle  is  a  peculiar  one,  being 
composed  of  three  or  more  parallel  strips  of  steel, 
mounted  upon  a  ring  of  aluminum,  and  trimmed  to 
form  a  circle.  Long  aluminum  pointers  are  attached 
to  this  disk.  The  needle  is  balanced  upon  a  steel 
point,  on  which  rests  an  agate.  The  weight  of  the 
needle  is  only  twenty  grains. 

"  The  coils  are  so  placed  that  the  current  runs  paral- 
lel with  the  meridian  of  the  needle.  They  are  half  an 
inch  or  more  wider  than  the  diameter  of  the  disk.  By 
this  means  all  parts  of  the  steel  composing  the  needle 
are  subjected  to  the  same  inductive  influence  in  all  its 
deflections. 

"  It  is  a  condition  indispensable  in  the  construction 
of  a  true  tangent  galvanometer,  that  the  current 
through  the  coil  should  act  as  uniformly  upon  the 
needle  in  all  its  deflections  as  the  earth's  magnetism 
does ;  a  narrow  coil  under  a  long  needle  does  not  ful- 
fill this  condition  ;  for,  as  the  extremities  of  the  needle 
in  its  deflections  pass  more  and  more  away  from  the 
coil,  the  inductive  influence  is  less  and  less,  as  com- 
pared with  the  earth's  influence. 


22  TANGENT  GALVANOMETER. 


"On  the  contrary,  if  we  place  a  very  broad  coil  un- 
der a  long  needle,  the  same  difficulty  occurs,  but  in 
the  opposite  direction.  While  the  needle  is  on  the 
meridian  it  is  under  the  influence  of  but  few  convolu- 
tions in  the  middle  of  the  coil,  but  as  it  deflects  it 
comes  under  the  influence  of  an  increasing  number  of 
convolutions,  and  therefore  the  influence  is  more  and 
more  increased. 

"  It  being  evident  that  the  truth  lay  between  these 
extremes,  the  expedient  of  a  needle  in  the  form  above 
described  was  resorted  to,  and  with  entire  success,  for 
in  this  the  condition  sought  is  accurately  fulfilled. 

"  Coil  No.  i  is  composed  of  very  fine  copper  wire, 
wound  evenly  back  and  forth  over  the  whole  width  of 
the  coil,  and  of  a  sufficient  number  of  layers  to  give  a 
resistance  of  150  or  more  ohms. 

"  No.  2  is  of  No.  30  wire  wound  in  the  same  manner, 
and  to  twenty-five  or  thirty  ohms  resistance.  No.  3  is 
of  two  layers  of  No.  23  wire,  giving  one  to  two  ohms 
resistance.  And  No.  4  is  a  strip  of  sheet  copper  of  the 
width  of  the  coils,  and  wound  three  and  a  half  times 
around,  so  that  the  current  passes  four  times  under 
the  needle ;  the  resistance  of  this  may  be  considered 
as  null,  or  not  sufficient  to  be  noticed  or  taken  into 
account. 

"  The  outer  ends  of  all  the  coils  are  connected  with 
a  common  screw-cup,  while  the  inner  ones  are  con- 
nected each  with  its  cup  bearing  its  proper  number. 

"  Coil  No.  1  is  for  currents  of  high  intensity,  No.  4  for 
those  of  great  quantity,  and  Nos.  2  and  3  are  for  mixed 
or  intermediate  currents. 

"  The  Rheostat  contains  coils  whose  several  resis- 
tances range  from  T-J-7  of  an  ohm  to  4000  ohms,  any 
one  or  more  of  which  may  be  thrown  into  the  circuit 
by  removing  the  proper  plug  or  plugs  on  the  top  of 
the  rheostat,  so  that  any  resistance  may  be  introduced 
from  ^-g-  of  an  ohm  to  10,000  ohms. 

"  In  addition  to  two  screw-cups  [I.  and  II.]  for  con- 


TANGENT  GALVANOMETER. 


nection  with  the  battery  and  galvanometer,  there  are 
two  other  screw-cups  [III.  and  IV.]  for  connection  of 


any  conductor  whose  resistance  it  is  intended  to  meas- 
ure ;  also  a  switch,  A,  on  the  rheostat,  so  arranged 
that  the  battery  may  be  thrown  through  the  rheostat 
or  the  conductor." 

CONNECTIONS  FOR  MEASUREMENT.— Connect  line  or 
instrument-wires  to  be  measured,  to  posts  III.  and  IV. 


24  TANGENT  GALVANOMETER. 


of  the  rheostat,  one  pole  of  the  battery  to  B,  on  the 
galvanometer,  and  the  other  to  I,  on  the  rheostat. 
The  wire  leading  from  II.  of  the  rheostat,  is  connected 
with  i,  2,  3,  or  4,  of  the  galvanometer,  depending  upon 
the  coil  to  be  used.  Push  the  switch  A  to  the  right, 
throwing  the  current  through  the  wire  to  be  measured. 
Note  the  deflection  of  the  needle.  Now  push  A  to  the 
left-hand  plate,  throwing  the  current  through  the 
rheostat.  Remove  plugs,  thus  letting  resistance  into 
circuit,  until  the  needle  shows  the  same,  deflection. 
Add  the  figures  marked  on  the  holes  unplugged,  and 
you  have  your  resistance  in  ohms. 

When  you  measure  a  wire  put  to  ground  at  distant 
end,  connect  as  before,  except  that  you  put  a  ground- 
wire  to  post  IV.,  and  line  to  III.  Manipulate  as 
before. 

TESTING  FOR  INSULATION.  —  First  unplug  10,000 
ohms  resistance,  using  galvanometer  coil  No.  i.  Note 
the  deflection  with  the  current  through  the  10,000 
ohms.  Call  this  the  "  maximum  of  the  galvanometer." 
Now  switch  to  the  line  (which  is  open  at  the  farther 
end),  and  note  the  deflection  again.  (The  better  the 
insulation  of  line  the  less  the  deflection.) 

Suppose  the  deflection  with  the  10,000  ohms  of  the 
rheostat  to  be  30°,  the  tangent  of  which  is  .5774*,  while 
that  through  the  line  is  10°,  the  tangent  of  which  is 
.1763. 

Now  the  tangent  .5774  is  to  10,000  ohms,  as  the  tan- 
gent .1763  inversely  is  to  the  answer;  or, 

.5774  x  10,000  hms> 

.1763 

the  insulation  resistance  of  the  line.  This,  multiplied 
by  the  number  of  miles,  gives  the  mileage  insulation, 
and  this  again,  by  the  number  of  insulators  per  mile, 
the  average  resistance  of  each  insulator. 

*  See  table  of  tangents. 


GAUGAIN  GALVANOMETER. 


We  give  the  above  examples  to  show  the  method  of 
using  the  instrument.  Many  of  the  formulae  given  in 
this  book  may  be  used  for  various  measurements  with 
this  instrument. 

2.  Gamgain  Galvanometer. — This  is  also  a  tan- 
gent instrument,  useful  for  measuring  the  electromo- 
tive force  of  batteries,  their  quantity  and  internal 
resistance.  Its  construction  is  in  accordance  with  the 
following  law : 

"  If  a  magnetized  needle  is  submitted  to  the  action 
of  a  circular  current,  placed  in  the  magnetic  meridian, 
when  the  center  of  the  needle  occupies  the  summit  of 
a  cone,  having  for  its  base  the  circular  current,  the 
tangents  of  the  angles  of  the  deviation  of  the  needle 
will  be  nearly  proportional  to  the  force  of  the  current, 
when  the  height  of  the  cone  is  equal  to  one-fourth  of 
the  diameter  at  its  base.  This  theorem  is  correct  within 
TOTT»  when  the  needle  is  from  1.17  inches  to  1.36  inches 
in  length,  and  the  coil  not  less  in  diameter  than  thrice 
the  length  of  the  needle." 

Fig.  2  (a,  b)  gives  a  plan  and  an  elevation  of  this  gal- 
vanometer. 

The  wire  forming  the  helix  is  generally  wound  in 
two  parts  of  equal  length  and  resistance,  thus  having 


FIG.  -3  (a).     Plan,  of  Gaugain  Galvanometer. 


26 


DIFFERENTIAL  GALVANOMETER. 


an  equal  effect  upon  the  needle.     Thus  this  galvano- 
meter may  be  used  with  both  coils  connected,  and  the 


FIG.  2  (3).     Elevation  of  Gaugain  Galvanometer. 

indication  given  by  the  deflection  as  in  a  tangent  in- 
strument, or  the  resistance  to  be  measured,  may  be 
connected  with  one-half,  and  a  rheostat  with  the  other, 
using  it  as  a  differential  instrument. 

3.  Differential  Galvanometer. — In  this  form  the 
needle  is  acted  upon  by  two  coils  of  equal   length, 


WHEATSTONE  BRIDGE. 


27 


resistance,  and  power.  The  current  leads  to  the  coils 
on  one  wire,  where  it  divides,  passing  around  the 
needle  in  opposite  directions.  The  resistance  to  be 
measured  is  attached  to  one  coil,  and  the  rheostat  to 
the  other.  When  the  same  amount  of  resistance  is  let 
into  circuit  in  the  rheostat,  or  its  equivalent  by  shunt- 
ing (see  shunt),  the  effect  upon  the  needle  will  be  the 
same  in  each  direction,  and  the  needle  will  be  brought 
to  zero.  Then  the  resistance  shown  in  the  rheostat 
(multiplied  by  the  shunt,  if  one  is  used,)  gives  the 
required  information. 

4.  Wlieatstone  Bridge. — In  tangent  and  differ- 
ential galvanometers  the  effect  upon  the  needle  is 
proportioned  to  the  strength  of  the  current,  this  being 
controlled,  of  course,  by  the  resistance  in  circuit.  The 
Wheatstone  Bridge  system  of  measurement  is  entirely 
different,  its  action  being  based  upon  the  fall  of  ten- 
sion of  the  current. 

The  fall  of  tension  of  a  current  from  the  pole  of  the 
battery  to  the  wire  terminal  at  the  ground  is,  as  we 
have  shown,  uniform.  If,  for  a  portion  of  the  distance, 
we  use  two  wires  instead  of  one,  the  current  will  di- 
vide and  flow  by  the  two  branches,  and  a  point  on  one 
wire  may  be  connected  to  a  point  on  the  other  by  a 
cross-wire,  where  the  tension  of  the  current  is  the 


28  THE  WHEATSTONE  BRIDGE. 


same,  without  at  all  affecting  the  flow  of  current  on 
the  two  lines.  For,  as  the  flow  of  current  is  caused  by 
a  difference  of  tension  between  the  battery  and  the 
point  with  which  it  is  connected  by  the  line-wire,  and 
as  the  tension  of  the  currents  at  the  two  points  on  the 
wires  connected  by  the  cross-wire  is  the  same,  no 
current  will  flow  through  the  cross-wire.  And  a  gal- 
vanometer inserted  in  this  cross-wire  will,  of  course, 
show  no  deflection. 

In  Fig.  3,  suppose  the  current  to  start  from  E  and 
flow  to  post  i>.  Here  it  divides,  one-half  passing  by 
wire  A,  3,  B,  to  2,  and  the  rest  by  C,  4,  D,  to  2,  and 
thence  the  current  returns  to  battery.  The  resistance 
of  the  sides,  A  and  C,  and  B  and  D,  being  alike,  the 
tension  of  the  two  portions  of  the  current,  at  3  and  4, 
is  the  same,  and  no  current  will  pass  across,  from  3  to 
4,  through  the  galvanometer. 

Again  :  suppose  we  insert  at  A  a  resistance  of  10,  at 
B  100,  at  C  500,  and  at  D  5000.  We  shall  find  that  the 
needle  on  the  cross-wire  still  refuses  to  deflect.  Be- 
cause the  current  divides  at"':i,  inversely  as  the  resist- 
ance of  the  two  routes  i,  A,.3<  and  i,  C,  4;  and  the 
resistance  at  C  being  50  times  as,  great  as  at  A,  50  parts 
of  the  current  passed  through1  A,  with  a  resistance  of 
10,  while  i  part  passed  through  C  with  a  resistance  of 
500.  The  tensions  of  the  two  portions,  on  arriving  at  3 
and  4,  are  the  same,  and  as  the  same  proportion  as 
between  A  and  C,  is  found  between  B  and  D,  the  divid- 
ed portions  pass  on  until  they  join  at  2  and  return  to 
battery.  Therefore,  when  A  bears  the  same  propor- 
tion to  C,  that  B  does  to  D,  or  when  A  :  C  : :  B  :  D,  no 
current  will  pass  between  3  and  4. 

Now  let  us  measure  an  unknown  resistance  which 
we  will  insert  between  the  binding-posts  at  D.  Say 
we  put  20  ohms  in  at  C,  and  i  at  A.  The  needle  is 
deflected  strongly.  Now  insert  resistance  at  B  until 
the  needle  comes  back  to  zero.  Say  it  requires  250 
units. 


THE  WHEATSTONE  BRIDGE.  29 


Then, 

20  x  250 

_L_  =  5000, 

which  is  the  resistance  at  D. 

If  the  resistance  to  be  measured  is  small,  you  may 
insert  equal  amounts  at  A  and  C,  and  then  the  number 
of  units  inserted  at  B  will  exactly  equal  D. 

There  are  two  forms  of  galvanometers  in  this  coun- 
try, made  on  the  above  principle :  Siemens'  and  Gray 
&*  Barton's.  The  latter  we  will  descif|n&  first,  as  its 
arrangement  is  similar  to  the  diagranWjng.  3. 

The  battery-wire  is  led  to  a  brass/bjMe,  on  each  side 
of  which'  are  smaller  plates  connecTSra  with  resistance 
coils.  By  inserting  plugs  on  eagjraitie  of  the  battery- 
plate,  the  proportions  of  resistaflye  between  the  first 
and  second  sides  of  the  bridg^JA.  and  C,  Fig.  3)  may 
be  varied  at  pleasure.  The  ifeflstance  to  be  measured 
is  introduced  at  D,  and  a  rhecWat  box  at  B. 

The  Siemens'  galvanometer  is  entirely  different  in 
appearance,  and  although/jfct  as  accurate  as  the  Gray 
&  Barton  for  small  measfljements,  is  much  more  con- 
venient for  general  lijfejwork,  as  it  is  portable,  light, 
and  convenient  in  form. 

The  needle  is  made  astatic.  That  is,  two  light  nee- 
dles are  affixed  rigidly  to  the  same  shaft.  The  two 
needles  are  polarized  in  different  directions.  One  be- 
ing slightly  stronger  than  the  other,  the  working  effect 
or  polarity  of  the  pair  is  the  difference  in  strength  be- 
tween them.  This  being  very  slight,  the  tendency  to 
remain  in  the  magnetic  meridian  is  very  feeble,  and  an 
extremely  weak  battery-current  will  cause  a  deflection. 
To  increase  still  more  the  sensitiveness  of  the  needle, 
it  is  suspended  by  a  single  fibre  of  untwisted  cocoon 
silk.  The  lower  needle  hangs  inside  the  coil,  while  the 
upper,  which  serves  also  for  an  indicator,  hangs  across 
the  top  of  the  dial.  The  dial  and  needle  are  covered 
with  a  glass  case  ;  surrounding  the  base  of  the  glass 


30  THE  WHEATSTONE  BRIDGE, 


horizontally  is  a  slate  disc,  divided  into  300  degrees, 
running  150  from  each  side  of  the  centre  or  o  mark. 
Half  embedded  in  the  edge  of  this  slate  is  a  platinum 
or  German-silver  wire.  This  wire  forms  the  first  and 
second  sides  of  the  Wheatstone  bridge — the  A  and  C 
of  Fig.  3. 

Pressing  against  this  wire  is  a  small  platinum  wheel, 
with  a  vernier,  on  a  movable  arm.  To  this  the  battery- 
wire  is  connected.  In  the  base  of  the  instrument  are 
three  resistance-coils,  10,  100,  and  1,000,  either  one  of 
which  is  let  into  the  third  side  (B,  Fig.  3)  by  removing 
the  plug  which  cuts  it  out.  The  resistance  to  be  meas- 
ured is  introduced  into  side  4  (D,  Fig.  3). 

The  principle  of  measurement  is  precisely  like  that 
shown  in  Fig.  3 ;  but  in  the  Siemens',  sides  B  and  D 
being  fixed,  you  vary  the  proportion  between  A  and  C 
until  the  proportion  of  the  latter  two  is  the  same  as  the 
first  two. 

The  slate  being  divided  into  two  parts  by  the  divi- 
sions of  150  each,  one  side  is  marked  A  and  the  other 
B.  Fig.  4  will  show  the  connections.  To  measure  the 
resistance  of  a  relay,  for  instance,  we  connect  the  bat- 
tery to  posts  I.  and  II.,  and  the  wires  from  the  resist- 
ance to  be  measured  to  posts  II.  and  IV.  The  plug  re- 
mains in,  between  III.  and  IV.  Remove  the  plug  at  100. 

The  current  passes  from  post  I.  to  roller  Z.  There 
it  divides,  one  portion  going  by  the  wire  on  the  edge 
of  the  slate,  through  the  resistance  coil  100  back  to 
battery,  by  post  II.  The  other  portion  of  the  current 
passes  (on  the  B  side  of  the  slate)  to  posts  III.  and  IV., 
thence  out  through  the  relay  to  be  measured,  and  back 
to  battery  at  post  II. 

Remember,  that  the  wire  between  the  roller  Z  and  150, 
on  one  side  of  the  slate,  is  the  first  side  (A,  Fig.  3) ;  that 
between  the  roller  and  1 50  on  the  opposite  side  corre- 
sponds with  the  second  side  (C,  Fig.  3) ;  the  resistance  100 
to  post  II.,  the  third  side  (B,  Fig.  3) ;  and  from  post  IV., 
through  the  relay  to  be  measured,  back  to  post  II.  (D, 


THE  WHEATSTONE  BRIDGE. 


Fig.  3),  is  the  fourth  side ;  while  from  C,  through  the 
galvanometer,  is  the  cross  or  bridge-wire. 


FIG.  4. 

Now,  when  by  moving  the  roller  Z  to  the  left  or 
right,  the  proportion  between  the  sides  of  the  slate,  A 
and  B,  is  the  same  as  between  the  resistance  100  and 
the  relay  to  be  measured,  the  needle  will  come  to  zero. 

Suppose  that  when  the  needle  stands  at  o,  the  wheel 
Z  is  at  50,  on  the  A  side  of  the  slate.  Then,  as  A  is  to 
B,  so  is  100  to  X,  the  unknown  resistance.  There  are 
1 50  degrees  on  each  half  of  the  slate.  Then  the  for- 
mula would  read, 


1 50  +  50 


x  100  =  X,     or 


150—50  100 

which  is  the  resistance  sought. 


x  loo  =  200 , 


32  SINE  GALVANOMETER. 


When  a  line  is  to  be  measured,  connect  battery  to 
post  I.,  ground  to  II.,  and  line  to  IV.  The  ground  on 
post  IJrcompletes  the  circuits,  as  the  line  is  grounded 
at  distant  end,  and  the  other  end  of  the  battery  is 
also  grounded. 

5.  Sine  Galvanometer. — The  strength  of  the  cur- 
rent, in  a  sine  galvanometer,  is  proportional  to  the  sine 
of  the  angle  of  deflection.  The  Siemens'  may  be  used 
as  a  sine  galvanometer  by  connecting  the  battery  to 
post  II.,  and  line  to  be  measured  to  IV.,  and  unplug- 
ging between  III.  and  IV.  Set  the  needle  in  position  ; 
put  the  vernier-wheel  at  o,  on  the  slate.  Now,  when 
the  needle  is  deflected,  move  the  needle-coil  by  revolv- 
ing the  slate  in  the  direction  of  the  deflection  of  the 
needle.  The  coil  is  thus  kept  parallel  with  the  needle, 
and  its  maximum  effect  exerted.  When  the  needle  is 
deflected  to  that  point  where  the  earth's  attraction  for 
the  needle  is  exactly  balanced  by  the  effort  of  the  coil- 
current  to  deflect  it,  the  needle  will  become  stationary. 
Now  read  the  degree  on  the  slate  opposite  the  vernier, 
and  a  reference  to  the  table  of  sines  will  give  the  sine 
of  the  deflection  ;  and  having  previously  taken  the 
constant  of  your  instrument — that  is,  having  found  to 
what  sine  it  will  deflect  with  a  given  resistance  and  a 
given  battery — you  have  now  a  proportion  giving  you 
the  result  sought. 


FORMULAE.  33 


CHAPTER    III. 

FORMULA: 

TO  MEASURE    ELECTROMOTIVE   FORCE  AND    INTERNAL    RESIST- 
ANCE  OF  A  BATTERY. 

1st.    By   Method   of  Equal    Deflections.—  The 

standard  cell  being  ..............................   E, 

The  one  to  be  compared  being  ...................   E'. 

Take  the  deflection  of  E  and  call  it  ...............   R, 

Then  take  the  deflection  of  E'  and  call  it  .........   R', 

Adding  resistance  to  make  the  deflection  the   same. 
Then, 


2d.    By  Direct  Measurement,   giving  also  the 
internal   resistance   of  the   battery   (with   Bradley  or 
Gaugain). 
First,  take  tangent  of  deflection,  without  resist- 

ance, call  it  ...............................         I 

Then  take  it  with  given  resistance  .............   =  I' 

Let  the  resistance  used  be  called  ...............        R 

The  resistance  of  galvanometer  ................   =  G 

And  of  the  battery  ............................        X  . 

For  the  electromotive  force,  multiply 

7by^+£,     or    fx(X+G)  =  E. 
And  the  internal  resistance  of  the  battery  is  found 


34  INTERNAL  RESISTANCE  OF  BATTERY. 


by   subtracting  the    resistance   of   the  galvanometer 
from 

72  x  R 


Example.  —  Suppose  the  resistance  of  the  galvano- 
meter to  be  .56  of  an  ohm. 

The  first  deflection  is  80°,  of  which  the  tangent  is  5.671 
With   10  ohms  resistance  it  is  52°,  of  which  the 

tangent  is  .................................  i  .280 

5.671  —  1.280  =  4.391  . 

Multiply  the  second  tangent,  1.280,  by  the  resistance, 
10,  and  we  have  12,800,  which,  divided  by  the  differ- 
ence between  the  two  tangents, 

12,800  , 

—  =2.96, 


which  is  the  total  resistance  in  circuit.  Deduct  the 
galvanometer  resistance,  .56,  and  we  have  the  internal 
resistance  of  the  battery,  =  2.40. 

The  tangent  of  I  was  5.671,  and  this,  multiplied  by 
the  total  resistance  in  circuit,  gives  16.78616  as  the 
electromotive  force  of  the  battery. 

Internal  Resistance  of  Battery.  —  Put  the  bat- 
tery in  circuit  with  a  sine  or  tangent  galvanometer. 
Note  the  deflection.  Halve  the  tangent  of  the  deflec- 
tion by  introducing  resistance.  The  resistance  intro- 
duced is  equal  to  the  original  resistance  —  that  of  the 
battery  and  the  galvanometer-coil.  Deduct  the  latter 
and  you  have  the  desired  result. 

Mance's  Formula,  —  A  and  B  are  two  resistances 


MEASUREMENT  OF  INSULATION. 


35 


whose  ratio  is  known.     R,  an  adjustable  rheostat ;  E, 
battery. 


FIG.  4. 

When  the  needle  is  balanced,  by  closing  wire  C  D 
atK, 

E-RA 

2?' 

This  is  regardless  of  the  resistance  of  the  galvano- 
meter. The  Wheatstone  bridge  may  be  used  for  this 
mode  of  measurement. 

Sir  Wm.  Thomson's  modification  of  the  above  gJ^es 
the  resistance  of  the  galvanometer  by  the  deflection  of 
its  own  needle.  Thus, 


FIG.  5. 
Balance  made  as  before. 


36        MEASUREMENT  OF  ELECTROMOTIVE  FORCE. 


Now  the  resistance  of  the  galvanometer,  G,  is, 

G=R-B- 

Measurement  of  Electromotive  Force  by 
Comparison.—  (Clark.)—  When  a  number  of  cells 
are  joined  up  in  circuit  with,  but  in  opposition  to,  a 
number  of  other  cells,  with  a  galvanometer  inserted, 
by  adjusting  the  number  of  cells  so  that  no  current 
passes,  the  relative  electromotive  force  of  the  two  bat- 
teries may  be  determined. 

Or,  call  the  electromotive  forces  of  the  two  batteries 
E  and  E'  ;  join  them  up  successively  in  circuit  with  the 
same  galvanometer,  and  by  varying  the  resistance 
cause  them  both  to  give  the  same  deflection  ;  their 
forces  will  then  be  in  direct  proportion  to  the  total 
resistances  in  circuit  in  each  case,  or, 


When  R  represents  the  resistance  with  E  (including 
that  of  battery,  galvanometer,  and  the  adjustable  resist- 
ance) and  R'  with  E'. 

Measurement  of  Insulation.  —  The  table  given 
on  page  7,  of  the  specific  resistances  of  metals,  might 
be  indefinitely  extended,  embracing  liquids  of  all 
kinds,  gums,  resins,  glass,  minerals,  etc.  Silver  and 
copper,  the  first  on  the  list,  represent  the  best  con- 
ductors, while  dry  air  ranks  lowest  as  a  conductor, 
and  therefore  highest  as  an  insulator,  insulation  being 
the  converse  of  conduction. 

The  insulating  power  of  any  material  with  reference 
to  a  given  current  depends  upon  the  tension  or  energy 
of  that  current.  The  less  the  tension,  the  less  power 
the  current  has  to  overcome  the  resistance  of  a  con- 
ductor; hence  water,  which  is  a  fair  conductor  of  the 
currents  used  on  ordinary  telegraph  lines,  is  an  ex- 
cellent insulator  for  currents  of  low  tension,  and  dry 


TESTING  FOR  INSULATION.  37- 


glass,  which  is  an  insulator  for  telegraphic  currents 
may  be  perforated  by  currents  of  sufficient  tension 
while  atmospheric  electricity  readily  overcomes  the 
resistance  of  dry  air.  Insulation  is,  therefore,  a  rela- 
tive term.  Now,  glass,  porcelain,  etc.,  are  absolute 
non-conductors  of  telegraphic  currents.  Theoreti- 
cally, therefore,  these  substances  should  be  perfect 
insulators  for  telegraphic  currents.  In  practice,  how- 
ever, glass,  and  in  a  less  degree  porcelain,  part  with 
heat  when  cooled  ;  hence  a  thin  film  of  water  con- 
densed from  the  moisture  of  the  air  forms  upon  the 
surface  of  each  insulator,  and  conducts  electricity 
from  the  wire  to  the  supports.  Upon  a  long  line  the 
total  leakage  from  the  great  number  of  insulators  is 
therefore  very  sensible.  Accumulations  of  dust  and 
smoke  upon  the  surface  of  an  insulator  absorb  and 
retain  moisture.  A  similar  effect  arises  from  the  webs 
of  insects  connecting  the  outside  of  the  insulator  with 
its  support. 

In  order  to  prevent  the  escape  from  the  direct  ac- 
tion of  rain,  a  flange  or  petticoat  is  formed  upon  the 
insulator,  giving  it  a  concave  under-surface.  During 
a  rainfall  this  is  the  only  serviceable  portion  of  the  insu- 
lator, as  the  exterior  is  covered  with  a  film  of  water. 
Thus  the  aggregate  escape  in  moist  weather  is  consi- 
derable, even  when  every  insulator  is  sound  ;  broken 
insulators,  of  course,  greatly  increase  the  leakage. 
Measurements  for  general  or  average  insulation  are, 
of  course,  valueless  when  there  is  a  great  leakage  at 
one  point.  If  the  line  is  opened  at  the  distant  end, 
and  the  deflection  of  the  galvanometer  shows  that  a 
current  still  flows  to  line,  it  is  obvious  that  it  must 
pass  to  ground  over  the  surface  of  the  insulators.  If 
the  escape  is  practically  uniform  along  the  line  it  may 
be  measured  thus: 


09 


38  TESTING  FOR  CONDUCTIVITY — LINE  RESISTANCE. 


Open  line  at  distant  end,  connect  your  battery  to 
line  throug)  the  galvanometer  ;  the  resistance  meas- 
ured and  calculated  in  the  usual  manner  will  be  the 
insulation-resistance  of  the  entire  line,  which  multi- 
plied by  its  length  in  miles  gives  the  mean  insulation- 
resistance  per  mile,  and  again  multiplied  by  the  num- 
ber of  poles  per  mile  gives  the  mean  resistance  per 
insulator. 

Explanation. — To  ascertain  wire-resistance,  divide 
the  total  resistance  by  the  length  in  miles,  because 
the  resistance  increases  in  proportion  to  the  length. 
To  ascertain  insulation-resistance  per  mile  multiply 
the  total  resistance  by  the  mileage,  because  the  es- 
cape increases  in  proportion  to  the  length,  two  miles 
giving  twice  the  escape,  and  hence  one-half  the  insu- 
lation of  one  mile. 

Testing  for  Conductivity. — First,  test  with  line 
open  at  distant  end,  for  if  there  is  a  heavy  escape  on 
the  line  your  resistance  will  show  less  than  it  really  is. 
Then  close  the  wire,  and  the  result  will  be  the  entire 
resistance  of  the  wire  and  instruments  (if  they  are  in 
circuit).  To  test  the  wire  carefully,  the  relays  should 
all  be  cut  out.  The  total  resistance,  divided  by  the 
number  of  miles,  gives  the  wire  resistance  per  mile. 

Line  Resistance  Measured  from  an  Interme- 
diate Station. — Mr.  F.  L.  Pope  gives  the  following 
ingenious  method  of  measurement  with  the  Bradley 
Tangent,  putting  it  into  circuit  anywhere  on  the  line. 
Any  good  tangent  could  be  used  in  the  same  manner: 

"  Connect  the  main  circuit  so  that  it  will  pass 
through  I.  and  II.  of  the  rheostat,  and  through  the  No. 
i  coil  of  the  galvanometer.  When  the  circuit  is  closed 
for  a  few  seconds  take  a  reading  of  the  deflection,  then 
unplug  a  sufficient  resistance  to  reduce  the  deflection 
perhaps  one-half  (1,000  or  2,000  ohms  will  usually  an- 


LINE  RESISTANCE.  39 


swer),  and  take  a  second  reading.  It  is  well  to  reverse 
the  connections  and  repeat  the  two  observations,  and 
take  the  mean  result  of  the  two  deflections.  The  fol- 
lowing example  will  serve  to  show  how  the  result  is 
worked  out : 

" '  Suppose  the  deflection  obtained  on  No.  i  coil  in 
the  main  circuit  is  61°  (tan.  1.804),  and  by  inserting 
2,000  ohms  it  is  reduced  to  42°  (tan.  .900).  If  we  call 
the  unknown  resistance  x,  we  have, 

x  :  x  4-  2000  : :  .900  (tan.  42°)  :  1.804  (tan.  61°)- 
Converting  this  into  an  equation  and  reducing, 
.904.3:  =  1800000 
x  =  1991.' 

"  Or  (to  avoid  equations),  subtract  the  tan.  of  42° 
(.900)  from  tan.  61°  (1.804)  and  we  have  .904  for  the 
equivalent  tan.  for  the  2000  ohms  inserted.  Now, 

"  Tan.  .904  :  2000  ohms  :  :  tan.  .900  :  1991  ohms. 

"The  resistance  of  all  relays  in  the  line  are,  of 
course,  to  be  subtracted." 

Corrected  One  Resistance  by  Schwendler. — 

This  is  only  applicable    to  a  line    having    a   general 
escape  its  entire  length.     In  such  case  you  obtain  the 
absolute  line  resistance,  irrespective  of  the  escape. 
Let, 

R  =  measured  insulation  resistance  of  line. 

r  =  wire  resistance  without  relay  at  distant  end. 

r'  —  wire  resistance  including  relay  at  distant  end. 

Then,  [i]  The  Corrected  Line-wire  resistance  L,  is, 
Z  =  2(7? 


40       LINE  RESISTANCE— TESTING  FOR  GROUNDS. 


[2]  The  Corrected  Insulation  resistance  R,  is, 


R  =  y  £  (£  -  r)  . 
[3]  The  Relay  resistance  r',    is, 

R(r'-r) 
R-r1    ' 

SECOND  METHOD. — 

R  =  apparent  insulation  resistance. 
r  =  apparent  conductivity. 

The  corrected  line  resistance  L,  will  be, 


This  is  based  on  the  supposition  that  the  entire 
escape  is  concentrated  at  one  point  midway  of  the  cir- 
cuit. Unless  the  line  is  very  long,  and  the  escape  ex- 
tremely bad,  this  formula  is  very  accurate.  And  on 
the  same  supposition  the  corrected  insulation  resist- 
ance, R',  will  be, 

R'  =  R--. 

2 

Testing*  for  Grounds. — ist.  FROM  EACH  END. — 
Having  a  record  of  the  mileage  resistance  of  the  wire, 
let  it  be  measured  from  each  end  to  the  fault. 

Call  the  registered  or  known  resistance  of  the  wire  R. 
Measurement  from  the  most  distant  end  through 

the  fault  to  ground  (other  end  open)     L. 

Ditto  from  the  opposite  end S. 

r> 

Then     L  +  S  —  —  =  G ,    the  resistance  of  the  fault ; 

L  —  G    gives   the  distance  of  long  end,  and     S  —  G 
distance  of  short  end  from  fault. 


TESTING  FOR  GROUNDS.  41 


2d.  BY  LOOP  TEST. —  With  Differential  Galvanome- 
ter.— Connect  two  wires  in  metallic  loop  at  distant  end. 
Measure  the  loop,  disregarding  the  fault.  Now  con- 
nect the  two  wires  to  the  two  circuits  of  the  galvano- 
meter, attaching-  battery  with  one  end  to  ground.  As 
one  wire  runs  to  the  station  beyond  the  fault,  and  re- 
turns to  the  fault  to  take  ground,  it  will  show  the  most 
resistance.  Put  resistance  in  the  other  side  to  balance. 
Call  this  resistance  b  ;  call  resistance  of  metallic  loop  a. 

Then  —  =     distance  from   measuring   station  on 

shortest  wire  to  fault. 

With  Tangent  Galvanometer.  —  ist.  Measure  loop, 
which  is  a. 

2d.  Take  deflection  on  longest  wire,  with  shortest 
open  at  your  instrument. 

3d.  Take  deflection  of  shortest  wire,  with  longest 
open.  Now  add  resistance  to  make  third  measurement 
equal  the  second.  Call  this  resistance  b. 

And  as  before,     =     distance  on  short  wire. 


With  Siemens ',  without  Rheostat. — (Haskms.) 

Call  resistance  of  metallic  loop a. 

Call  measurement  of  longest  part  of  loop b. 

Call  measurement  of  shortest  part  of  loop c. 

Call  resistance  of  fault d. 

And  distance  of  fault  from  office x. 


b  +  c  —  a 

_ =  d,     and     c  —  d  —  x 


or,     b  —  c—g,     the  difference  between  the  two  legs 
of  the  loop  ;  and, 


42  TESTING  FOR  CROSSES. 


3d.   FROM  ONE  END.—  (Blavier.) 

Call  the  registered   or   known    resistance   of   the 

wire   R. 

Measure  with  further  end  closed  (current  escaping 

-      also  by  the  fault) S. 

Then  measure  open  at  distant  end.     Call  this T. 

Call  distance  of  fault X. 

And  resistance  of  fault. .  .   Z. 


^=5  —  <J (R—S)  x  T-S, 
and, 


Z=  T—S+  <\/jR-Sx  T—S. 

Testing:  4"or  Crosses. — Both  wires  being  substan- 
tially alike,  or  their  resistance  known. 


FIG.  6. 

i st.   Measure  A  to  B  (C  and  D  open),  call  it F. 

2d.    Measure  A  to  D  (C  and  B  open),  call  it G. 

3d.    Measure  A  to  C  (B  and  D  open),  call  it H. 

G  —  F=  R    (resistance  of  cross) R. 

and, 

=  distance  to  R . 


With  any  Galvanometer  and  Rheostat,  by  Bridge  Meth- 
od.— First,  with  B  and  D,  Fig.  5,  open,  measure  the 
metallic  loop  ;  call  it  L. 

Now  connect  the  galvanometer  as  a  bridge,  making 
A  to  X  one  side  of  the  bridge,  and  C  to  X  another 
side.  Lead  two  wires,  a  and  3,  of  equal  resistance,  to 
A  and  C,  from  battery. 


TESTING  FOR  CROSSES. 


FIG.  7. 

Add  resistance  at  rheostat,  to  balance 
and  cross  at  X.     Call  this  resistance  R. 

L  —  R       *  .     TT. 


f! 


or,  if  A  to  X  is  greater  than  the  other 
cross,  put  resistance  in  at  C  instead,  and, 


When  resistance  of  wires  is  not  alike.- 


e  C  to  X, 


and  the 


FIG.  8. 

Measure  A  to  B,  call  it F. 

C  to  B,  call  it G. 

A  to  C,  call  it H. 

E  to  B,  call  it K. 

"         Resistance  of  cross,  call  it R. 


44  TESTING  FOR  CROSSES. 


Y+R  +  K=G 
X-  Y=F-G+ 

X  +  Y=H-R 


Example.  —  Suppose  F  =  2000, 
"        G  =  2750, 
"        H=3ioo. 
Then, 

H         F          G 
3100  -f  2000  —  2750  =  2350  . 

2^=2350,     and    -^=1175. 
The  distance,  then,  from  A  to  E  is  1175. 

With  Siemens'  Galvanometer.  —  (Sargent^)  —  Measure 
loop  ;  call  it  L.  Ground  the  wire  to  be  measured  at 
distant  end,  and  connect  it  to  post  IV.  Open  the  other 
wire  at  farther  end,  and  connect  it  to  II.  Battery  to  I. 
Leave  all  plugs  in.  Take  B  side  of  slate  for  reading, 
and  A  +  B  :  B  :  :  L  to  X  ,  wire  attached  to  IV. 

Example.  —  Suppose  each  wire  to  measure,  to  the 
cross,  1000  ohms,  and  the  cross  to  measure  500  ohms. 
Then  the  loop  measurement  would  be  2500  ohms. 

To  balance,  the  vernier  would  stand  at  30°  on  the  B 
side.  There  being  300  degrees  on  the  slate,  B  would 
read  120°.  And  as  300  is  to  120,  so  is  2500  to  the  an- 
swer. 

•  —  =  .4  x  2500  =  looo  , 

300 

the  distance  to  the  cross. 


TESTING  BAD  GROUNDS— SHUNTS.  45 


Testing  Bsul  Grounds.  —  When  you  suspect  that 
a  ground-wire  at  a  distant  terminal-station  is  imper- 
fect, you  can  test  it  by  two  methods. 

i  st.  Measure  two  lines  to  earth,  through  suspected 
ground  ;  then  loop  the  wires  at  that  station,  and  meas- 
ure the  metallic  loop.  If  the  sum  of  the  two,  measured 
to  ground,  exceed  the  resistance  of  the  metallic  loop, 
then  the  excess,  divided  by  2,  will  give  the  resistance 
of  the  faulty  ground. 

2d.  To  ascertain  merely  whether  a  ground  is  faulty, 
should  one  line  be  so  busy  that  it  could  not  well  be 
spared,  connect  another  wire  to  the  suspected  ground- 
wire,  between  the  battery  terminal  and  the  ground. 
Put  your  galvanometer  to  the  other  end  of  this  wire, 
with  a  good  ground.  If  the  suspected  ground  is  really 
faulty,  the  current  will  divide  where  the  second  wire  is 
attached,  and  flow  over  the  second  wire,  deflecting 
your  needle. 

Shunts.  —  The  multiplying  power  of  a  shunt  is  equal 
to 

-—  ,     or     y  +  i, 

g  being  the  resistance  of  the  galvanometer,  and  s  that 
of  the  shunt. 

To  prepare  a  shunt  having  some  definite  multiply- 
ing power,  let  n  equal  the  power  required,  and 


n  —  I 

Example.  —  Suppose  the  resistance  of  the  galvano- 
meter to  be  loo  units,  and  a  shunt  is  desired  having  a 
multiplying  power  of  1000, 

Then      s  =  —  —  —  =  .0999+. 

1000  +    I 

The  joint  resistance  of  a  galvanometer  and  shunt  is 


46  UNITS  OF  MEASUREMENT— WIRES. 


found  by  the   rule  for  finding  joint  resistance  of  de- 
rived or  parallel  circuits.     Thus, 

g  =  resistance  of  galvanometer. 
s  =  resistance  of  shunt. 

Then      /?  =  -^— . 
g  +  s 

Units  of  Measurement. — 

Megohm  =  1,000,000  Ohms. 

Ohm          =  1,000,000  Microhms. 

Varley       =  25  Ohms. 

Siemens    =  0.9536        •* 

Ohm          =  1.0486  Siemens. 

Wires. —  The  Weight  of  any  Iron  wire,  per  mile  of 

5280  feet,  is ,     d  being-  the   diameter  of  wire  in 

72.15 

mils,  or  thousandths  of  an  inch. 

The  Conductivity  of  Iron  wire,  galvanized,  is  from 
\  to  T}-  pure  copper. 

The  Resistance  of  Iron  wire,  per  mile,  is  about  - — - — 

ohms,  at  60°  Fahr.     It  increases  about  .35  per  cent,  for 
each  degree  Fahr. 

The  Diameter  of  any  Iron  wire,  weighing  w  Ibs.  per 
|  statute  mile,  is 

8.49  \/w  .  .  .  mils. 

I  Iron  expands  T^|T-^  of  its  length,  or  about  411ff  inches 
per  mile  for  every  10°  heat. — Cullcy. 

The  Weight  per  mile  of  Copper  wire  is    7 Ibs. 

The  Resistance  of  any  pure  Copper  wire,  per  mile,  is, 
at  60- Fahr., 


WEIGHT  OF  WIRE— SPECIFIC  RESISTANCE. 


47 


The  Resistance  of  any  pure   Copper  wire  /  inches 

.001516  x  r    . 
long,  weighing  n  grains,  is ohms. 

The  resistance  increases  for  .21  per  cent,  for  each 
degree  Fahr. 

The  Diameter  of  any  Copper  wire,  weighing  w  Ibs. 
per  statute  mile,  is  7. 94^/2^  .  .  .  mils. 

The  Conductivity  of  any  Copper  wire  is  obtained  by 
multiplying  its  calculated  resistance  by  100,  and  divid- 
ing the  product  by  its  actual  resistance.  Pure  Copper 
taken  as  100. — (Clark.) 

Weight  of  Insulated  OlSace  Wire.— - 

N.B. — These  weights  are  only  approximately  correct,  as  different  samples 
of  the  same  wire  vary  somewhat  from  each  other. 


DESCRIPTION. 


Number 
of  core. 


Feet 
per Ib. 


Kerite  Compound „ 27 

Kerite  Copper 14  33 

Kerite  Copper . .  16  50 

Gutta  Percha 14  55 

Paraffined  Cotton  and  Hemp 14  55 

Braided  Cotton 12  44 

Braided  Cotton 14  57 

Braided  Cotton 16  86 

Phillips' Braided  and  Painted 14  50 

Phillips'       do.  do 16  50 

Phillips'       do.  do 20  75 

Specific  Resistance  of  Different  Metals— Com- 
pared with  pure  copper. 

Copper i.oo    Tin  wire 6.80 

Silver 98    Zinc  wire 3.70 

Gold 1.13    Brass  wire 3.88 

Iron 5.63    German-silver  wire . .  1 1 .30 

\  Lead  10.76    Nickel  wire 7.70 

|  Mercury 50.00    Cadmium  wire 2.61 

Palladium  wire 5.50    Aluminum  wire 1.75 

Platinum  6.78  I  (M.  G.  Farmer.) 


48 


WEIGHT  AND  RESISTANCE  OF  WIRES. 


Table    of  Weight  and  Resistance  of   Copper 

Wires. 

[This  Table  was  prepared  and  kindly  furnished  by  DR.  E.  A.  HILL,  of 

Chicago.] 

Taking  for  a  unit  a  wire  one  mil  (T15Vo  inch)  in  diam- 

eter, and  one  foot  in  length,  the  following  figures  give 

a  numerical  expression  for  the  weights  and  resistances 

of  copper,  iron,  and  German-silver  wires. 

Copper.                 Iron.              German-silver. 

Weights,      .000003028      .00000265      .00000296  Ibs. 

Resistances,      9.94                59.1              127.32  ohms. 

WEIGHT  PER  FOOT, 

RESISTANCE  PER  FOOT, 

Diameter 

IN  POUNDS. 

IN   OHMS. 

in  mils. 

Pure  Copper, 

German- 

Pure  Copper, 

German- 

hard  drawn. 

silver. 

hard  drawn. 

silver. 

X 

.  000003028 

.00000296 

9.94 

127.32 

2 

.000012 

.000012 

2.485 

31-83 

3 

.000027 

.000027 

i  .  10444 

14.14666 

4 

.000048 

.000047 

.62125 

7-95625 

.000075 

.000074 

.39760 

5.09280 

6 

.000109 

.000107 

.27611 

3-53666 

7 

.000148 

000145 

.20285 

2.59836 

8 

.000193 

.000189 

.1553* 

1.98906 

9 

.000245 

.000240 

.12272 

1.57181 

10 

.000303 

.000296 

.09940 

2.27320 

ii 

.000366 

.000358 

.08214 

i  05223 

12 

.000436 

.000426 

.06002 

.88416 

13 

.000512 

.000500 

.05881 

•75337 

14 

.000593 

.000580 

.05071 

.64969 

IS 

.000681 

.000666 

.04417 

.56586 

16 

.000775 

.000758 

.03887 

•49734 

17 

.000875 

000855 

•03439 

.44055 

18 

.000981 

.000959 

.03062 

.39296 

19 

.001094 

.001069 

.02753 

.35268 

20 

.001212 

.001184 

.02485 

.31830 

21 

.001336 

001305 

.02253 

.28848 

22 

.001466 

.001433 

.02053 

.  26305 

23 

.001002 

.001566 

.01879 

.  24068 

24 

.001745 

.001705 

.01725 

.22104 

25 

.001893 

.001850 

.01590 

.20371 

26 

.002048 

.002001 

.01470 

.18834 

27 

.002208 

.002158 

.01363 

•17465 

28 

.002375 

.002321 

.01267 

.16239 

29 

.002548 

.002489 

.01181 

.15139 

30 

.002727 

.002664 

.01104 

.14146 

.002911 

.002845 

.01034 

.13248 

32 

.003102 

.003031 

.00970 

.12444 

33 

.003299 

.003223 

.00912 

.11691 

34 

.003502 

.003422 

.00859 

.11013 

WEIGHT  AND  RESISTANCE  OF  WIRES. 


49 


Table    of  Weight   and  Resistance  of  Copper 

Wires.  —  Concluded. 

WEIGHT  PER  FOOT, 

RESISTANCE  PER  FOOT, 

Diameter 

IN  POUNDS. 

IN  OHMS. 

in  mils. 

Pure  Copper, 

German- 

Pure  Copper, 

German- 

hard  drawn. 

silver. 

hard  drawn. 

silver. 

35 

.003711 

.003626 

.00811 

•10393 

36 

.  003926 

.003836 

.00766 

.09824 

38 

.004375 

.004274 

.00688 

.08754 

40 

.004848 

.004736 

.00621 

.07956 

42 

•005344 

.005221 

.00563 

.07217 

8 

.005868 
.006411 

.005731 
.006263 

.00513 
.00469 

.06576 
.06017 

48 

.006981 

.006820 

.00431 

.05526 

50 

•007575 

.007400 

.00399 

.05009 

55 

.009165 

.008954 

.00330 

.04208 

60 

.010908 

.010656 

.00276 

•03519 

65 

.012801 

.012506 

.00235 

.03013 

70 

.014847 

.014504 

.00202 

.02598 

75 

.017043 

.016650 

.00176 

.02263 

80 

.019392 

.018944 

.00155 

.01989 

Iron. 

Iron  annealed 

85 

.021991 

.01915 

.00137 

.00818 

90 

•024543  . 

.02146 

.00122 

.00729 

95 

•027345 

.02392 

.00110 

.00655 

100 

.030280 

.02650 

000994 

.00591 

no 

.036663 

.03206 

.000821 

.00488 

120 

.043632 

.03816 

.000690 

.00410 

I30 

.051207 

.04478 

.000588 

.00349 

140 

.059388    , 

•05794 

.000507 

.00301 

ISO 

.068175 

.05962 

.000441 

.00262 

160 

.077568 

.06784 

.000389 

.00230 

170 

.087567 

.07658 

.000344 

.00204 

1  80 

.098172 

.08686 

.000306 

.00185 

190 

.  109383 

.09566 

.000275 

.00163 

200 

.I2I2OO 

.10600 

.000249 

.00147 

Electromotive   Force  of  Batteries. 

Compared  with  Grove. 

Grove  100 

Carbon,  with  bichromate  (electropoion)  solution.  .    107 

Daniel,  Hill,  and  Callaud  56 

When  put  on  short  circuit,  the  carbon  battery  polar- 

izes  rapidly,    hydrogen    gathering    upon   the   carbon 

more  rapidly  than  the  bichromate  can  absorb  it. 

NATURAL  TANGENTS. 


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SINES  AND  TANGENTS. 


Table  of  Sines  and  Tangents. 

Deg. 

Sine. 

Tangent. 

Deg. 

Sine. 

Tangent. 

0.5 

00873 

00872 

29 

48481 

55430 

i 

01745 

01745 

29-5 

49242 

56577 

i-5 

02618 

02618 

30 

50000 

57735 

2 

03490 

03492 

30.5 

50754 

58904 

2.5 

04362 

04366 

31 

51504 

60086 

3 

05234 

05240 

31-5 

52250 

61280 

3-5 

06105 

06116 

32 

52992 

62486 

4 

06796 

06992 

32  5 

53730 

63707 

4-5 

07846 

07870 

33 

54464 

64940 

5 

08716 

08748 

33-5 

55194 

66188 

5-5 

09585 

09628 

34 

55919 

67450 

6 

i°453 

10510 

34-5 

56641 

68728 

6-5 

11320 

"393 

35 

57358 

70020 

7 

12187 

12278 

35-5 

58070 

71321 

7-5 

13053 

I3l65 

36 

58779 

72654 

8 

i39J7 

14054 

36.5 

59482 

73996 

8-5 

14781 

14945 

37 

60182 

75355 

9 

15643 

^5838 

37-5 

60876 

76732 

9-5 

16505 

l6734 

38 

61566 

78128 

10 

17365 

17632 

38.5 

62251 

79543 

10.5 

18224 

i8533 

39 

62932 

80978 

ii 

19081 

19438 

39-5 

63608 

82433 

"•5 

19937 

20345 

40 

64279 

83910 

12 

20791 

21255 

40-5 

64945 

85408 

12.5 

21644 

22169 

4i 

6^606 

86928 

*3 

22945 

23086 

4i-5 

66262 

88472 

J3-5 

23345 

24007 

42 

66913 

90040 

*4 

24192 

24932 

42-5 

67559 

9l633 

14.5 

23038 

25861 

43 

68200 

93251 

15 

25882 

26794 

43-5 

688^5 

15-5 

26724 

27732 

44 

69466 

96568 

16 

27564 

28674 

44-5 

70091 

98269 

16.5 

28402 

29621 

45 

70711 

.00000 

17 

29237 

30573 

45-5 

7*3»S 

.01761 

17-5 

30071 

31529 

46 

7*934 

•03553 

18 

30902 

32492 

46.5 

7^537 

.05378 

18.5 

3^30 

33459 

47 

73r35 

.07237 

19 

32557 

34432 

47-5 

73728 

09131 

19-5 

3338i 

354i  * 

48 

74314 

.11061 

20 

34202 

36397 

48.5 

74896 

.  13029 

20.5 

35°2i 

37388 

49 

75471 

•15037 

21 

~  "35*37 

38386 

49-5 

76041 

.17085 

21.5 

36650 

"  3$39*W.,.\ 

go 

76604 

•I9I75 

22 

3746i 

40402  *j-"-. 

\  5°*5 

77162 

.21310 

22.5 

38268 

41421 

5i 

777]5 

.23490 

23 

39°73 

42447 

5i-5 

'78261 

.2-717 

23-5 

39875 

4348i 

52 

78801 

.27994 

24 

40674 

44522 

52.5 

79335 

.30323 

24-5 

41469 

45572 

53 

79864 

32704 

25 

42262 

46630 

53-5 

80386 

•35H2 

25-5 

43051 

47697 

54 

80902 

•37638 

26 

43837 

48773 

54-5 

81412 

•40195 

26.5 

44620 

49858 

55 

81915 

.42815 

27 
27.5 

45399 
46i75 

50952 
52056 

55  5 
56 

82413 
82904 

.45501 
.48256 

28 

38.5 

46947 
47716 

53  *  7° 
54295 

56.5 
57 

5 

.51084 
.53987 

SINES  AND  TANGENTS. 


55 


Table  of  Sines  and  Tangents.  —  Concluded. 

Deg. 

Sine. 

Tangent. 

Deg. 

Sine. 

Tangent. 

57-5 

84339 

56969 

74 

96126 

3.48741 

58 

84805 

.60033 

74-5 

96363 

3.60588 

58.5 
59 

85264 
85717 

.63185 
.66428 

75 
75-5 

96593 
96815 

3-73205 
3.86671 

59-5 

86163 

.69766 

76 

97030 

4.01078 

60 

86603 

•73205 

76.5 

9/237 

4.16530 

60.5 

87036 

.76749 

77 

97437 

4-33H8 

61 

87462 

.80405 

77-5 

97630 

4-51071 

61.5 

87882 

.84177 

78 

97815 

4  .  70463 

62 

88295 

.88073 

78.5 

97992 

4.91516 

62.5 

88701 

.92098 

79 

98163 

5-14455 

63 

89101 

.96261 

79-5 

98325 

5-39552 

63-5 
64 
64-5 

89493 
89879 
90259 

.00569 
.  05030 
.09654 

80 
80.5 
81 

98481 
90629 
98769 

5.67128 
5-97S76 
6.3*375 

65 

90361 

81.5 

98902 

6.69116 

65.5 

90996 

•  1943° 

82 

99027 

7-IJ537 

66 
66.5 

91355 
91706 

.24604 
.29984 

82.5 
83 

99144 

99255 

7-59575 
8.14435 

67 

92050 

•35585 

83-5 

99357 

8.77689 

67-5 

92388 

.41421 

84 

99452 

9.5I436 

68 

92718 

.47509 

84.5 

9954° 

10.3854 

68.5 

& 

69-5 

93042 
93358 
93367 

•53865 
.60509 
.67462 

85 
85-5 
86 

99619 
99692 
99756 

11.4301 

12  .  7062 
14  .  3007 

70 

93969 

74748 

86.5 

16.3409 

70.5 

94264 

.  82391 

87 

99863 

94552 
94832 

.90421 
.98869 

87-5 
88 

99905 
99939 

22.9038 
28  .  6363 

72 

95106 

3-07768 

88.5 

99966 

38.1885 

72.5 
73 

95372 

3-i7i59 
3.27085 

89 
89-5 

99985 
99996 

57.7900 
II4    589 

73-5 

95882 

3-37594 

90 

lOOOOO 

~~~ 

56    bIZE,    WEIGHT,    KESISTANCE,    ETC.,    OF   IRON    WIRE. 


Table  of  the  Sizes,  Weights,  Resistances,  and 
Breaki&ig   Strain  of  Iron   Wires. 


No.  of  wire, 
B.  W.  G. 

Diam.  in 
mils, 
B.  W.  G. 

PER  STATUTE  MILE. 

Breaking 
strain, 
soft  wire. 

American 
gauge 
diameter. 

Weight 
in  Ibs. 

Resistance 
in  ohms. 

i  sq.  inch, 
i  circ.  u 
oooo 

1  7,645 
13^58 
2,854 

0.340 
o-433 

2.10 

1000 

•  454 

460 

ooo 

00 
0 

.425 
.380 
•340 

2,502 

2,001 
1,  6oO 

2.40 

3  o° 

3-74 

8600"' 
7100 

.40964 
.36480 
.32495 

I 

2 

3 

.300 
.284 
•  259 

1,245 
1,117 
928 

4.81 

5-37 
6.46 

6000 
4850 
4000 

.28930 

•25763 
.22942 

4 

.238 

.220 
.203 

783 
670 
570 

7-65 
8.96 
10.52 

3400 
2950 
2500 

.20431 
.  18194 
.  16202 

I 

9 

.l8o 
.165 
.148 

448 
376 
303 

13-38 
16.39 
19.79 

22OO 
1750 
1500 

.14428 
.12849 
.IJ443 

10 
ii 

12 

•134 
.I2O 
.109 

249 
199 
l64 

24.14 

30.10 
36.49 

I20O 
820 
7IO 

.10189 
.09074 
.08081 

The  Birmingham  wire-gauge  is  really  not  one  gauge, 
but  an  approximation  only,  as  different  manufacturers 
do  not  agree  in  sizes.  The  American  gauge  is  formed 
upon  a  geometrical  progression.  The  last  column  of 
the  above  table  gives 'the  American  gauge  diameter 
of  the  various  numbers. — (For  the  figures  in  this  col- 
umn we  are  indebted  to  Pope's  Modern  Practice,  page 
146.)  The  columns  of  weight,  breaking-strain,  and 
resistance,  all  refer  to  wire  of  Birmingham  gauge. 


TABLE  OF  SQUARES,  CUBES,   SQUARE  AND  CUBE  KOOTS, 


Number. 

Squares. 

Cubes. 

s/Koots. 

v^  Roots. 

Reciprocals. 

1 

1 

1 

1-0000000 

1-0000000 

l.ooooooot 

2 

4 

8 

1-4142136 

1-2599210 

•500000000 

3 

9 

27 

1-7320508 

1-4422496 

•333333333 

4 

16 

64 

2-0000000 

1-5874011 

•250000000 

5 

25 

125 

2-2360680 

1-7099759 

•200000000 

6 

36 

216 

2-4494897 

1-8171206 

•166666667 

7 

49 

343 

2-6457513 

1-9129312 

•142857143 

8 

64 

512 

2-8284271 

2-0000000 

•125000000 

9 

81 

729 

3-0000000 

2-0800837 

•111111111 

10 

100 

1000 

3-1622777 

2-1544347 

•100000000 

11 

121 

1331 

3-3166248 

2-2239801 

•090909091 

12 

144 

1728 

3-4641016 

2-2894286 

•083333333 

13 

169 

2197 

3-6055513 

2-3513347 

•076923077 

14 

196 

2744 

3-7416574 

2-4101422 

•071428571 

15 

225 

3375 

3-8729833 

2-4662121 

•066666667 

16 

256 

4096 

4-0000000 

2-5198421 

•062500000 

17 

289 

4913 

4-1231056 

2-5712816 

•058823529 

18 

324 

5832 

4-2426407 

2-6207414 

•055555556 

19 

361 

6859 

4-3588989 

2-6684016 

•052631579 

20 

400 

8000 

4-4721360 

2-7144177 

•050000000 

21 

441 

9261 

4-5825757 

2-7589243 

•047619048 

22 

484 

10648 

4-6904158 

2-8020393 

•045454545 

23 

529 

12167 

4-7958315 

2-8438670 

•043478261 

24 

576 

13824 

4-8989795 

2-8844991 

•041666667 

25 

625 

15625 

5-0000000 

2-9240177 

•040000000 

26 

676 

17576 

5-0990195 

2-9624960 

•038461538 

27 

729 

19683 

5-1961524 

3-0000000 

•037037037 

28 

784 

21952 

5-2915026 

3-0365889 

•035714286 

29 

841 

24389 

5-3851648 

3-0723168 

•034482759 

30 

900 

27000 

5-4772256 

3-1072325 

•033333333 

31 

961 

29791 

5-5677644 

3-1413806 

•032258065 

32 

1024 

32768 

5-6568542 

3-1748021 

•031250000 

33 

1089 

35937 

5-7445626 

3-2075343 

•030303030 

34 

1156 

39304 

5-8309519 

3-2396118 

•029411765 

35 

1225 

42875 

5-9160798 

3-2710663 

•028571429 

36 

1296 

46656 

6-0000000 

3-3019272 

•027777778 

17 

1369 

50653 

6-0827625 

3-3322218 

•027027027 

38 

1444 

54872 

6-1644140 

3-3619754 

•026315789 

39 

1521 

59319 

6-2449980 

3-3912114 

•025641026 

40 

1600 

64000 

6-3245553 

3-4199519 

•025000000 

41 

1681 

68921 

6-4031242 

3-4482172 

•024390244 

42 

1764 

74088 

6-4807407 

3-4760266 

•023809524 

43 

1849 

79507 

6-5574385 

3-5033981 

•023255814 

44 

1936 

85184 

6-6332496 

3-5303483 

•022727273 

45 

2025 

91125 

6-7082039 

3-5568933 

•022222222 

46 

2116 

97336 

6-7823300 

3-5830479 

•021739130 

47 

2209 

103823 

6-8556546 

3-6088261 

•021276600 

48 

2304 

110592 

6-9282032 

3-6342411 

•020833333 

49 

2401 

117649 

7-0000000 

3-6593057 

•020408163 

50 

2500 

125000 

7-0710678 

3-6840314 

•020000000 

51 

2601 

132651 

7-1414284 

3-7084298 

•019607843 

62 

2704 

140608 

7-2111026 

3-7325111 

•019230769 

TAELS  or  SQUARES,  CUBES,  SQUARE  AND  CUBE  ROOTS. 


Number.  Squares. 

Cubes. 

<J  Roots. 

•V/  Roots. 

Reciprocals. 

53  ,  2809 

148877 

7-2801099 

3-7562858 

-01S867925 

54 

2916 

157464 

7-3484692 

3-7797631 

•018518519 

55 

3U25 

166375 

7-4161985 

3-8029525 

•018181S18 

56 

3136 

175616 

7-4833148 

3-S25S624 

•017857143 

57 

3249 

185193 

7-5498344 

3-8485011 

•017543S60 

58 

3364 

190112 

7-6157731 

3-8708766 

•017241379 

59 

3481 

205379 

7-6811467 

3-8929965 

•016949153 

60 

3600 

216000 

7-74596G7 

3-9148676 

•01666C667 

61 

3721 

226981 

7-8102497 

3-9304972 

•016393-143 

62 

3844 

238328 

7-8740079 

3-9578915 

•016129032 

63 

3909 

250047 

7-9372539 

3-9790571 

•015873016 

64 

4096 

262144 

8-0000000 

4-0000000 

•015625000 

65 

4225 

274625 

8-0622577 

4-0207256 

•015384615 

66 

4356 

287496 

8-1240384 

4-0412401 

•015151515 

67 

4489 

300763 

8-1853528 

4-0615480 

•014925373 

68 

4624 

314432 

8-2462113 

4-0816551 

•014705882 

69 

4761 

328509 

8-3066239 

4-1015661 

•014492754 

70 

4900 

343000 

8-3666003 

4-1212853 

•014285714 

71 

5041 

357911 

8-4261498 

4-1408178 

•014084517 

72 

5184 

373248 

8-4852814 

4-1601676 

•013888889 

Y3 

5329 

3S9017 

8-5440037 

4-1793390 

•013698630 

74 

5476 

405224 

8-6023253 

4-1983364 

•013513514 

75 

5625 

421875 

8-6602540 

4-2171633 

•013333333 

76 

5776 

438976 

8-7177979 

4-2358236 

•013157895 

77 

5929 

456533 

8-7749644 

4-2543210 

•012987013 

78 

6084 

474552 

8-8317609 

4-2726586 

•012820513 

79 

6241 

493039 

8-8881944 

4-2908404 

•012658228 

80 

6400 

512000 

8-9442719 

4-3088695 

•012500000 

81 

6561 

531441 

9-0000000 

4-3267487 

•012345679 

82 

6724 

551S68 

9-0553851 

4-3444815 

•012195122 

83 

6889 

571787 

9-1104336 

4-3620707 

•012048193 

84 

7056 

592704 

9-1651514 

4-3795191 

•011904762 

85 

7225 

614125 

9-2195445 

4-3968296 

•011764706 

86 

7396 

636056    9-2736185 

4-4140049 

•011627907 

87 

7569 

658503 

9-3273791 

4-4310476 

•011494253 

88 

7744 

681472 

9-3803315 

4-4479692 

•011363636 

89 

7921 

704969 

9-4339811 

4-4647451 

•011235955 

90 

8100 

729000 

9-4868330 

4-4814047 

•011111111 

91 

8281 

753571 

9-5393920 

4-4979414 

•010989011 

92 

8464 

778688 

9-5916630 

4-5143574 

•010869565 

93 

8649 

804357 

9-6436508 

4-5306549 

•010752688 

94 

8836 

830584 

9-6953597 

4-5468359 

•010638298 

95 

9025 

857375 

9-7467943 

4-5629026 

•010536316 

96 

9216 

884736 

9-7979590 

4-5788570 

•010416667 

97 

9409 

912673 

9-8488578 

4-5947009 

•010309278 

93 

9604 

941192 

9-8994949 

4-6104363 

•010204082 

99 

9801 

970299 

9-9498744 

4-6260650 

•010101010 

100 

10000 

1000000 

10-0000000 

4-6415888 

•010000000 

101 

10201 

1030301 

10-0498756 

4-6570095 

•009900990 

102 

10404 

1061208 

10-0995049 

4-6723287 

•009803922 

103 

10609 

1092727 

10-1488916 

4-6875482 

•009708738 

104 

10816 

1124864 

10-1980390 

4-7025694 

•009615385 

TABLE  OP  SQUARES,  CUBES,  SQUAXB  AND  CUBE  ROOM 


Number. 

Squares. 

Cubes. 

V^Roots. 

V'  Hoots.  '* 

Reciprocals. 

105 

11025 

1157625 

10-2469508 

4-7176940 

•0095^810 

106 

11236 

1191016 

J  0-2956301 

4-732G235 

•009432962 

107 

11449 

1225043 

10-3440804 

4-7474594 

•009345794 

108 

11664 

1259712 

10-0923048 

4-7622032 

•009259259 

109 

11881 

1295029 

10-4403065 

4-7768562 

•009174312 

no 

12100 

1331000 

10-4880885 

4-7914199 

•009090CG9 

111 

12321 

1367631 

10-5356538 

4-S05SS95 

•009009009 

112 

12544 

1404928 

10-5830052 

4-8202845 

•00892S571 

113 

12769 

1442S97 

10-6301458 

4-S345SS1 

•OOSS49558 

114 

12996 

1481544 

10-6770783 

4-S48S076 

•OOS771930 

115 

13225 

1520875 

10-7238053 

4-8629442 

•008695652 

116 

13456 

1560896 

10-7703296 

4-8769990 

•008620690 

117 

13689 

1601613 

10-8166538 

4-8909732 

•008547009 

118 

13924 

1643032 

10-8627805 

4-9048681 

•008474576 

119 

14161 

1685159 

10-9087121 

4-9186847 

•008403361 

120 

14400 

1728000 

10-9544512 

4-9324242 

•008333333 

121 

14641 

1771561 

11-0000000 

4-9460874 

•008264463 

122 

14834 

1815848 

11-0453610 

4-9596757 

•008196721 

123 

15129 

1860867 

11-0905365 

4-9731898 

•0081300S1 

124 

15376 

1906624 

11-1355287 

4-9866310 

•008064516 

125 

15625 

1953125 

11-1803399 

5-0000000 

•008000000 

126 

15876 

2000376 

11-2249722 

5-0132979 

•007936508 

127 

16129 

2048383 

11-2694277 

5-0265257 

•007874016 

128 

16384 

2097152 

11-3137085 

5-0396842 

•007812500 

129 

16641 

2146689 

11-3578167 

5-0527743 

•007751938 

130 

16900 

2197000 

11-4017543 

5-0657970 

•007692308 

131 

17161 

2248091 

11-4455231 

5-0787531 

•007633588 

132 

17424 

2299968 

11-4891253 

5-0916434 

•007575758 

133 

17689 

2352637 

11-5325626 

5-1044687 

•007518797 

134 

17956 

2406104 

11-5758369 

5-1172299 

•007462687 

135 

18225 

2460375 

11-6189500 

5-1299278 

•007407407 

136 

18496 

2515456 

11-6619038 

5-1425632 

•007352941 

137 

18769 

2571353 

11-7046999 

5-1551367 

•007299270 

138 

19044 

2628072 

11-7473401 

5-1676493 

•007246377 

139 

19321 

2685619 

11-7898261 

5-1801015 

•007194245 

140 

19600 

2744000 

11-8321596 

5-1924941 

•007142857 

141 

19881 

2803221 

11-8743421 

5-2048279 

•007092199 

142 

20164 

2863288 

11-9163753 

5-2171034 

•007042254 

143 

20449 

292*207 

11-9582607 

5-2293215 

•006993007 

144 

20736 

2985984 

12-0000000 

5-2414828 

•006944444 

145 

21025 

3048625 

12-0415946 

5-2535879 

•006896552 

146 

21316 

3112136 

12-0830460 

5-2656374 

•006849315 

147 

21609 

3176523 

12-1243557 

5-2776321 

•006802721 

148 

21904 

3241792 

12-1655251 

5-2895725 

•006756757 

149 

22201 

3307949 

12-2065556 

5-3014592 

•006711409 

150 

22500 

3375000 

12-2474487 

5-3132928 

•006666667 

151 

22801 

3442951 

12-2882057 

5-3250740 

•006622517 

152 

23104 

3511008 

12-3288280 

5-3368033 

•006578947 

153 

23409 

3581577 

12-3693169 

5-3484812 

•006635948 

154 

23716 

3652264 

12-4096736 

5-3601084 

•006493506 

155 

24025 

3723875 

12-4498996 

5-3716854 

•006451613 

156 

24336 

3796416 

12-489996U 

5-3832126 

•006410256 

TABLE  OP  SQUARES,  CUBES,  SQUARE  AND  CUBE  ROOTS. 


Number. 

Squares. 

Cubes. 

V  Eoota. 

V  Roots. 

Reciprocals. 

157 

24649 

3869893 

12-5299641 

5-3946907 

•006369427 

158 

24964 

3944312 

12-5698051 

5-4061202 

•006329114 

159 

25281 

4019679 

12-6095202 

5-4175015 

•006289308 

160 

25600 

4096000 

12-6491106 

5-4288352 

•006250000 

161 

25921 

4173281 

12-6885775 

5-4401218 

•006211180 

162 

26244 

4251528 

12-7279221 

5-4513618 

•006172840 

163 

26569 

4330747 

12-7671453 

5-4625556 

•006134969 

164 

26896 

4410944 

12-8062485 

5-4737037 

•006097561 

165 

27225 

4492125 

12-8452326 

5-4848066 

•006060606 

166 

27556 

4574296 

12-8840987 

5-4958647 

•006024096 

167 

27889 

4657463 

12-9228480 

5-5068784 

•005988024 

168 

28224 

4741632 

12-9614814 

5-5178484 

•005952381 

169 

28561 

4826809 

13-0000000 

5-5287748 

•005917160 

170 

28900 

4913000 

13-0384048 

5-5396583 

•005882353 

171 

29241 

5000211 

13-0766968 

5-5504991 

•005847963 

172 

20584 

5088448 

13-U48770 

5-5612978 

•005813953 

173 

29929 

5177717 

13-1529464 

5-5720546 

•005780347 

174 

30276 

5268024 

13-1909060 

5-5827702 

•005747126 

175 

30625 

5359375 

13-2287566 

5-5934447 

•005714286 

176 

30976 

5451776 

13-2664992 

5-6040787 

•005681818 

177 

31329 

5545233 

13-3041347 

5-6146724 

•005649718 

178 

31684 

5639752 

13-3416641 

5-6252263 

•005617978 

179 

32041 

5735339 

13-3790882 

5-6357408 

•005586592 

180 

32400 

5832000 

13-4164079 

5-6462162 

•005555556 

181 

32761 

5929741 

13-4536240 

5-6566528 

•005524862 

182 

33124 

6028568 

13-4907376 

5-6670511 

•005494505 

183 

33489 

6128487 

13-5277493 

5-6774114 

•005464481 

184 

33856 

6229504 

13-5646600 

5-6877340 

•005434783 

185 

34225 

6331625 

13-6014705 

5-6980192 

•005405405 

186 

34596 

6434856 

13-6381817 

5-7082675 

•005376344 

187 

34969 

6539203 

13-6747943 

5-7184791 

•005347594 

188 

35344 

6644672 

13-7113092 

5-7286543 

•005319149 

189 

35721 

6751269 

13-7477271 

5-7387936 

•005291005 

190 

36100 

6859000 

13-7840488 

5-7488971 

•005263158 

191 

36481 

6967871 

13-8202750 

5-7589652 

•005235602 

192 

36864 

7077888 

13-8564065 

5-7689982 

•005208333 

193 

37249 

7189517 

13-8924400 

5-7789966 

•005181347 

194 

37636 

7301384 

13-9283883 

5-7889604 

•005154639 

195 

38025 

7414875 

13-9642400 

5-7988900 

•005128205 

196 

38416 

7529536 

14-0000000 

5-8087857 

•005102041 

197 

38809 

7645373 

14-0356688 

5-8186479 

•005076142 

198 

39204 

7762392 

14-0712473 

5-8284867 

•005050505 

199 

39601 

7880599 

14-1067360 

5-8382725 

•005025126 

200 

40000 

8000000 

14-1421356 

5-8480355 

•005000000 

201 

40401 

8120601 

14-1774469 

5-8577660 

•004975124 

202 

40804 

8242408 

14-2126704 

5-8674673 

•004950495 

203 

41209 

8365427 

14-2478068 

5-8771307 

•004926108 

204 

41616 

8489664 

14-2828569 

5-8867653 

•004901961 

205 

42025 

8615125 

14-3178211 

5-8963685 

•004878049 

206 

42436 

8741816 

14-3527001 

5-9059406 

•004854369 

207 

42849 

8869743 

14-3874946 

5-9154817 

•004830918 

208 

43264 

8998912 

14-4222051 

5-9249921 

•004807692 

TABLE  OP  SQUARES,  CUBES,  SQUARE  AND  CUBE  ROOTS. 


Number. 

Squares 

Cubes. 

V  Roots. 

V'  Roots. 

Reciprocals. 

209 

43681 

9129329 

14-4568323 

5-9344721 

•004784689 

210 

44100 

9261000 

14-4913767 

6-9439220 

•004761905 

211 

44521 

9393931 

14-5258390 

5-9533418 

•004739336 

212 

44944 

9528128 

14-5602198 

5-9627320 

•00471698J 

213 

45369 

9663597 

14-5945195 

5-9720926 

•004694836 

214 

45796 

9800344 

14-6287388 

5-9814240 

•004672897 

215 

46225 

9938375 

14-6628783 

5-9907264 

•004651163 

216 

46656 

10077696 

14-6969385 

6-0000000 

•004629630 

217 

47089 

10218313 

14-7309199 

6-0092450 

•004608295 

213 

47524 

10360232 

14-7648231 

6-0184617 

•004587156 

219 

47961 

10503459 

14-7986486 

6-0276502 

•004566210 

220 

48400 

10648000 

14-8323970 

6-0368107 

•004545455 

221 

48841 

10793861 

14-8660687 

6-0459435 

•004524887 

222 

49284 

10941048 

14-8996644 

6-0550489 

•004504505 

223 

49729 

11080567 

14-9331845 

6-0641270 

•004484305 

224 

50176 

11239424 

14-9666295 

6-0731779 

•004464286 

225 

50625 

11390625 

15-0000000 

6-C824020 

•004444444 

226 

51076 

11543176 

15-0332964 

6-0991994 

•004424779 

227 

51529 

116970S3 

15-0665192 

6-1001702 

•004405286 

228 

51984 

11852352 

15-0996689 

6-1091147 

•004385965 

229 

52441 

12008989 

15-1327460 

6-1180332 

•004366812 

230 

52900 

12167000 

15-1657509 

6-1269257 

•004347826 

231 

53361 

12326391 

15-1986842 

6-1357924 

•004329004 

232 

53824 

12487168 

15-2315462 

6-1446337 

•004310345 

233 

54289 

12649337 

15-2643375 

6-1534495 

•004291845 

234 

54756 

12812904 

15-2970585 

6-1622401 

•004273504 

235 

55225 

12977875 

15-3297097 

6-1710058 

•004255319 

236 

55G96 

13144256 

15-3622915 

6-1797466 

•004237288 

237 

56169 

13312053 

15-3948043 

6-1884628 

•004219409 

233 

56644 

13481272 

15-4272486 

6-1971544 

•004201681 

239 

57121 

13651919 

15-4596248 

6-2058218 

•004184100 

240 

57600 

13824000 

15-4919334 

6-2144650 

•004166667 

241 

58081 

13997521 

15-5241747 

6-2230843 

•004149378 

242 

53564 

14172488 

15-5563492 

6-2316797 

•004132231 

243 

59049 

14348907 

15-5884573 

6-2402515 

•004115226 

244 

59536 

14526784 

15-6204994 

6-2487998 

•004098361 

245 

60025 

14706125 

15-6524758 

6-2573248 

•004081633 

216 

60516 

14886936 

15-6843871 

6-2658266 

•004065041 

247 

61009 

15069223 

15-7162336 

6-2743054 

•004048583 

248 

61504 

15252992 

15-7480157 

6-2827613 

•004032258 

249 

62001 

15438249 

15*<  797oo8 

6-2911946 

•004016064 

250 

62500 

15625000 

15-8113883 

6-2996053 

•004000000 

251 

63001 

15S13251 

15-8429795 

6-3079935 

•003984064 

252 

63504 

16003008 

15-8745079 

6-3163596 

•003968254 

253 

64009 

16194277 

15-9059737 

6-3247035 

•003952569 

254 

64516 

16387064 

15-9373775 

6-3330256 

•003937008 

255 

65025 

16581375 

15-9687194 

6-3413257 

•003921569 

256 

65536 

16777216 

16-0000000 

6-3496042 

•00390G250 

257 

66049 

16974593 

16-0312195 

6-3578611 

•003S91051 

258 

66564 

17173512 

16-0623784 

6-3660968 

•003875969 

259 

67081 

17373979 

16-00347G9 

6-3743111 

•003861004 

260 

67600. 

17576000 

16-1245155 

6-3825043 

•003846154 

IABLE  OF  SQUARES.  CUBES,  SQUARE  AKD  CUB*  ROOTS. 


Number. 

Squares. 

Cubes. 

V  Koots. 

y~R,oots. 

Reciprocals. 

261 

68121 

17779581 

16-1554944 

6-3906765 

•003831418 

262 

68644 

17984728 

16-1864141 

6-3988279 

•003S16794 

263 

69169 

18191447 

16-2172747 

6-4069585 

•003802281 

264 

69696 

18399744 

16-2480768 

6-4150687 

•003787879 

265 

70225 

18609625 

16-2788206 

6-4231583 

•003773585 

266 

70756 

18821096 

16-3095064 

6-4312276 

•003759398 

267 

71289 

19034163 

16-3401346 

6-4392767 

•003745318 

268 

71824 

19248832 

16-3707055 

6-4473057 

•003731343 

2G9 

72361 

19465109 

16-4012195 

6-4553148 

•003717472 

270 

72900 

19683000 

16.4316767 

6-4633041 

•003703704 

271 

73441 

19902511 

16-4620776 

6-4712736 

•003690037 

272 

73984 

20123643 

16-4924225 

6-4792236 

•003676471 

273 

74529 

20346417 

16-5227116 

6-4871541 

•003663004 

274 

75076 

20570824 

16-5529454 

6-4950653 

•003649635 

275 

75625 

20796S75 

16-583  J  240 

6-5029572 

•003636364 

276 

7G176 

21024576 

16-6132:77 

6-5108300 

•003623188 

277 

76729 

21253933 

16-6433170 

6-5186839 

•003610108 

278 

77284 

21484952 

16-6783320 

6-5265189 

•003597122 

279 

77841 

21717639 

16-7032931 

6-5343351 

•0035S4229 

2SO 

78400 

21952000 

16-7332005 

6-5421326 

•003571429 

281 

78961 

221S8GU 

16-7630540 

6-5499116 

•00355S719 

2S2 

79524 

224257CS 

16-7928556 

6-5576722 

•003546099 

2S3 

80089 

22665187 

16-8220038 

6-5654144 

•003533569 

2S4 

80656 

22900304 

1C  8522995 

6-5731385 

•003521127 

285 

81225 

23149125 

16'SS19430 

6-5808443 

•003508772 

286 

81796 

23093656 

16-9115345 

6-5885323 

•003496503 

287 

82369 

23639903 

16-9410743 

6-5962023 

-003484321 

288 

82944 

23887872 

16-9705627 

6-6038545 

•003472222 

239 

83521 

24137569 

17-0000000 

6-6114890 

•003460208 

290 

84100 

24389000 

17-0293G64 

6-6191060 

•003448276 

291 

84681 

24642171 

17-0587221 

6-0267054 

•003436426 

292 

85264 

24897088 

17-0880075 

6-6342874 

•003424658 

293 

85849 

25153757 

17-H7242S 

6-6418522 

•003412969 

294 

86436 

25412184 

17-1404282 

6-6493998 

•003401361 

295 

87025 

25672375 

17-1755610 

6-6069302 

•003389831 

206 

87016 

25934S36 

17-2046505 

6-C644437 

•003378378 

297 

88209 

2619S073 

17*2336879 

6-6719403 

-003367003 

293 

88804 

26463502 

17-2626765 

6.G794200 

•003355705 

299 

89401 

26730899 

17-2916165 

6.6868831 

•003344482 

SCO 

90000 

27000000 

17-32050S1 

6.6943295 

•003333333 

301 

90601 

272709C1 

17-3493516 

6.7017593 

•003322259 

302 

91204 

27543608 

17-3781472 

6-7091729 

•003311258 

303 

91S09 

27818127 

17-4068952 

6-71  6£%0 

•003301330 

304 

92416 

280944G4 

17-4355953 

6-7239508 

•003289474 

305 

93025 

2S372025 

17-4642402 

6-7313155 

•003278689 

306 

93636 

2S652616 

17-4928557 

6-7386641 

•003267974 

307 

94249 

281  34443 

17-5214155 

6-7459967 

•003257329 

308 

94864 

29218112 

17-5499283 

6-7533134 

•003246753 

309 

954S1 

29503609 

17-5783953 

6-7606143 

•003236246 

310 

96100 

29791000 

17-606S1C9 

6-7678995 

•003225806 

311 

93721 

30080231 

17-6351921 

6-7751690 

•003215434 

312 

97344 

30371328 

17-6635217 

6-7824229 

•003205128 

TABLE  OP.  SQUARES,  CUBES,  SQUARE  AND  CUBE  ROOTS. 


Number. 

Squares. 

Cubes. 

\/  Rooti. 

v'  Roots. 

Reciprocals. 

313 

9796& 

30664297 

17-6918060 

6-7896613 

•003194883 

314 

98596 

30959144 

17-7200451 

6-7968844 

•003184713 

315 

99225 

31255875 

17-7482393 

6-8040921 

•003^74603 

316 

99856 

31554496 

17-7763888 

6-8112847 

•003164557 

317 

100489 

31855013 

17-8044938 

6-8184620 

.003154574 

318 

101124 

32157432 

17-8325545 

6-8256242 

•003144ft£fc 

319 

101761 

32461759 

17-8605711 

6-8327714 

•00313478B" 

320 

102400 

32768000 

17-8885438 

6-8399037 

•003125000: 

321 

103041 

33076161 

17-9164729 

6-8470213 

•003115265 

322 

103684 

33386248 

17-9443584 

6-8541240 

•003105590 

323 

104329 

33698267 

17-9722008 

6-8612120 

•003095975 

324 

104976 

34012224 

18-0000000 

6-8682855 

•003086420 

325 

105625 

34328125 

18-0277564 

6-8753433 

•003075923 

326 

106276 

34645976 

18-0554701 

6-8823888 

•003067485 

327 

106929 

34965783 

18-0831413 

6-8894188 

•003048104 

328 

107584 

35287552 

18-1107703 

6-8964345 

•003048780 

329 

108241 

35611289 

18-1383571 

6-9034359 

•003039514 

330 

108900 

35937000 

18-1650021 

6-9104232 

•003030303 

331 

109561 

36264691 

18-1934054 

6-9173964 

•003021148 

332 

110224 

36594368 

18-220*6V2 

6-9243556 

•003012048 

333 

110889  1  36926037 

18-2482876 

6-9313088 

•003003003 

334 

111556  37259704 

18-2756689 

6-9382321 

•002994012 

335 

112225  137595375 

18-3030052 

6-9451496 

•002985075 

336 

112896  137933056 

18-3303028 

6-9520533 

•002976190 

337 

113569  138272753 

18-3575598 

6-9589434 

•002967359 

338 

114244  138614472 

18-3847763 

6-9658198 

•002U58580 

339 

114921  138958219 

18-4119526 

6-9726826 

•002949853 

340 

115600  139304000 

18-4390889 

6-9795321 

•002941176 

341 

116281  139651821 

18-4661853 

6-9863681 

•002932551 

342 

116964  140001688 

18-4932420 

6-9931906 

•002923977 

343 

117649  40353607 

18-5202592 

7-0000000 

•002915452 

344 

118336  140707584 

18-5472370 

7-0067962 

•002906977 

345 

119025  !  41063625 

18-5741756 

7-0135791 

•002898551 

346 

119716  41421736 

18-6010752 

7-0203490 

•002890173 

347 

120-109  41781923 

18-6279360 

7-0271058 

•002881844 

348 

121104  42144192 

18-6547581 

7-0338497 

•002873563 

349 

121801  42508549 

18-6815417 

7-0405860 

•002865330 

350 

122500  42875000 

18-7082869 

7-0472987 

•002857143 

351 

123201  43243551 

18-7349940 

7-0540041 

•002849003 

352 

123904  43614208 

18-7616630 

7-0606967 

•002840909 

353 

124609 

43986977 

18-7882942 

7-0673767 

•002832861 

354 

125316 

44361864 

18-8148877 

7-0740440 

•002824859 

355 

126025 

44738875 

18-8414437 

7-0806988 

•002816901 

356 

126736 

45118016 

18-8679623 

7-0873411 

•002808989 

357 

127449 

45499293 

18-8944436 

7-0939709 

•002801120 

358 

128164 

45882712 

18-9208879 

7-1005885 

•002793296 

359 

128881 

46268279 

18-9472953 

7-1071937 

•002785515 

360 

129600 

46656000 

18-9736660 

7-1137866 

•002777778 

361 

130321 

47045831 

19-0000000 

7-1203674 

•002770083 

362 

131044 

47437928 

19-0262976 

7-1269360 

•002762431 

363 

131769 

47832147 

19-0525589 

7-1334925 

•002754821 

364  1 

132496 

48228544 

19-0787840 

7-1400370 

•002747253 

TA*M  OP  SQUARES,  CUBES,  SQUARE  AND  CUBE  ROOTS. 


Number.  Squares 

Cubes. 

V  Roots. 

«y  Roots. 

Reciprocals. 

365 

133225 

48627125 

19-1049732 

7-1465695 

•002739726 

366 

133956  49027896 

19-1311265 

7-1530901 

•002732240 

367 

134689  49430863 

19-1572441 

7-1595988 

•002724796 

368 

135424 

4?836032 

19-1833261 

7-1660957 

•002717391 

369 

136161 

50243409 

19-2093727 

7-1725809 

•002710027 

370 

136900 

50653000 

19-2353841 

7-1790544 

•002702703 

371 

137641 

51064811 

19-2613603 

7-1855162 

•002695418 

372 

138384 

51478848 

19-2873015 

7-1919663 

•002688172 

373 

139129 

51895117 

19-3132079 

7-1984050 

•002680965 

374 

139876 

52313624 

19-3390796 

7-2048322 

•002673797 

375 

140625 

52734375 

19-3649167 

7-2112479 

•002666667 

376 

141376 

53157376 

19-3907194 

7-2176522 

•002659574 

377 

142129 

53582633 

19-4164878 

7-2240450 

•002652520 

378 

142884 

54010152 

19-4422221 

7-2304268 

•002645503 

379 

143641 

54439939 

19-4679223 

7-2367972 

•002638521 

380 

144400 

54872000 

19-4935887 

7-2431565 

•002631579 

381 

145161 

55306341 

19-5192213 

7-2495045 

•002624672 

382 

145924 

55742968 

19-5448203 

7-2558415 

•002617801 

383 

146689 

56181887 

19-5703858 

7-2621675 

•002610966 

384 

147456 

56623104 

19-5959179 

7-2684824 

•002604167 

385 

148225 

57066625 

19-6214169 

7-2747864 

•002597403 

386 

148996 

57512456 

19-6468827 

7-2810794 

•002590674 

387 

149769 

57960603 

19-6723156 

7-2873617 

•002583979 

388 
389 

150544,58411072 
151321  '58863869 

19-6977156 
19-7230829 

7-2936330 
7-2998936 

•002577320 
•002570694 

390 

152100 

59319000 

19-7484177 

7-3061436 

•002564103 

391 

152881 

59776471 

19-7737199 

7-3123828 

•002557545 

392 

153664 

60236288 

19-7989899 

7-3186114 

•002551020 

393 

154449 

60698457 

19-8242276 

7-3248295 

•002544529 

394 

155236 

61162984 

19-8494332 

7-3310369 

•002538071 

395 

156025 

61620875 

19-8746069 

7-3C72339 

•002531646 

396 

156816 

62099136 

19-8997487 

7-3434205 

•002525253 

397 

157609 

62570773 

19-9248588 

7-3495966 

•002518892 

398 

158404 

63044792 

19-9499373 

7-3557624 

•002512563 

399 

159201 

63521199 

19-9749844 

7-3619178 

•002506266 

400 

160000 

64000000 

20-0000000 

7-3680630 

•002500000 

401 

160801 

64481201 

20-0249844 

7-3741979 

•002493766 

402 

161604 

64964808 

20-0499377 

7-3803227 

•002487562 

403 

162409 

65450827 

20-0748599 

7-3864373 

•002481390 

404 

163216 

65939264 

20-0997512 

7-3925418 

•002475248 

405 

164025 

66430125 

20  1246118 

7-3986363 

•002469136 

406 

164836 

66923416 

20-1494417 

7-4047206 

•002463054 

407 

165649 

67419143 

20-1742410 

7-4107950 

•002457002 

408 

166464 

67917312 

20-1990099 

7-4168595 

•002450980 

409 

167281 

68417929 

20-2237484 

7-4229142 

•0024449S8 

410 

168100 

68921000 

20-2484537 

7-4289589 

•002439024 

411 

168921 

69426531 

20-2731349 

7-4319938 

•002433090 

412 

169744 

69934528 

20-2977831 

7-4410189 

•002427184 

413 

170569 

70444997 

20-3224014 

7-4470343 

•002421308 

414 

171396 

70957944 

20-3469899 

7-4530399 

•002415459 

415 

172225 

71473375 

20-3715488 

7-4590359 

•002409639 

416  I 

173056 

71991296 

20-3960781 

7-4650223 

•002406846 

TABLE  OF  SQUAWS,  CUBES,  SQUARE  AND  CUBE  ROOTS. 


8  umber. 

Squares. 

Cubes. 

V/  Roots. 

\/  Roots. 

Reciprocals. 

417 

L73889 

72511713 

20-4205779 

7-4709991 

•002398082 

418 

174724 

73034632 

20-4450483 

7-4769664 

•002392344 

419 

175561 

73560059 

20-4694895 

7-4829242 

•002386635 

420 

176400 

74088000 

20-4939015 

7-4888724 

•002380952 

421 

177241 

74618461 

20-5182845 

7-4948113 

•002375297 

422 

178084 

75151448 

20-5426386 

7-5007406 

•002369668 

423 

178929 

75686967 

20-5669638 

7-5066607 

•002364066 

424 

J79776 

76225024 

20-5912603 

7-5125715 

•002358491 

425 

180625 

76765625 

20-6155281 

7-5184730 

•002352941 

426 

181476 

77308776 

20-6397674 

7*5243652 

•002347418 

427 

182329 

77854483 

20-6639783 

7-5302482 

•002341920 

428 

183184 

78402752 

20-6881609 

7-5361221 

•002336449 

429 

184041 

78953589 

20-7123152 

7-5419867 

•002331002 

430 

184900 

79507000 

20-7364414 

7-5478423 

•002325581 

431 

185761 

80062991 

20-7605395 

7-5536888 

•002320186 

432 

186624 

80621568 

20-7846097 

7-5595263 

•002314815 

433 

187489 

81182737 

20-8086520 

7-5653548 

•002309469 

434 

188356 

81746504 

20-8326667 

7-5711743 

•002304147 

435 

189225 

82312875 

20-8566536 

7-5769849 

•002298851 

436 

190096 

82S81856 

20-8806130 

7-5827865 

•002293578 

437 

190969 

83453453 

20-9045450 

7-5885793 

•002288330 

438 

191844 

84027672 

20-9284495 

7-5943633 

•002283105 

439 

192721 

84604519 

20  9523268 

7-6001385 

•002277904 

440 

193600 

85184000 

20-9761770 

7-6059049 

•002272727 

441 

194481 

85766121 

21-0000000 

7-6116626 

•002267574 

442 

195364 

86350888 

21-0237960 

7-6174116 

•002262443 

443 

196249 

86938307 

21-0475652 

7-6231519 

•002257336 

444 

197136 

87528384 

21-0713075 

7-6288837 

•002252252 

445 

198025 

88121125 

21-0950231 

7-6346067 

•002247191 

146 

198916 

88716536 

21-1187121 

7-6403213 

•002242152 

447 

199809 

89314623 

21-1423745 

7-6460272 

•002237136 

448 

200704 

89915392 

21-1660105 

7-6517247 

•002232143 

449 

201601 

90518849 

21-1896201 

7-6574138 

•002227171 

450 

202500 

91125000 

21-2132034 

7-6630943 

•002222222 

451 

203401 

91733851 

21-2367606 

7-66£7665 

•002217295 

452 

204304 

92345408 

21-2602916 

7-6744303 

•002212389 

453 

205209 

92959677 

21-2837967 

7-6800857 

•002207506 

454 

206116 

93576664 

21-3072758 

7-6857328 

•002202643 

455 

207025 

94196375 

21-3307290 

7-6913717 

•002197802 

456 

207936 

94818816 

21-3541565 

7-6970023 

•002192982 

457 

208849 

95443993 

21-3775583 

7-7026246 

•002188184 

458 

209764 

96071912 

21-4009346 

7*7082388 

•002183406 

459 

210681 

96702579 

21-4242853 

7-7188448 

•002178649 

460 

211600 

97336000 

21-4476106 

7*7194426 

•002173913 

431 

212521 

97972181 

21-4709106 

7-7250325 

•002169197 

462 

213444 

98611128 

21-4941853 

7-7306141 

•002164502 

463 

214369 

99252847 

21-5174348 

7-7361877 

•002159827 

464 

215296 

99897344 

21-5406592 

7-7417532 

•002155172 

465 

216225 

100544625 

21-5638587 

7-7473109 

•OG2150538 

466 

217156 

101194696 

21-5870331 

7-7528606 

•002145923 

467 

218089 

101847563 

21-6101828 

7-7584023 

•002141328 

468 

219024 

102503232 

21-6333077 

7-7639361 

•0021367*2 

TABUS  o*  SQUARES.  CUBES,  SQUARE  AXD  CUBE  ROOM. 


Number. 

Squares. 

Cubes. 

>/Koots. 

4/JRoots. 

Reciprocals. 

469 

219961 

103161709 

21-6564078 

7-7C94620 

•002132196 

470 

220900 

103823000 

21-6794834 

7-7749801 

•002127060 

471 

221841 

104487111 

21-7025344 

7-7804904 

•002123142 

472 

222784 

105154048 

21-7255610 

7-7859928 

•002118644 

473 

223729 

105828817 

21-7485632 

7-7914875 

•002114165 

474 

224C76 

106496424 

21-7715411 

7-7969745 

•002109705 

475 

225625 

107171875 

21-7944947 

7-8024538 

•002105263 

476 

226576 

107850176 

21-8174242 

7-8079254 

•002100840 

477 

227529 

108531333 

21-8403297 

7-8133892 

•002096486 

478 

228484 

109215352 

21-8632111 

7-8188456 

•002092050 

479 

229441 

109902239 

21-8860686 

7-8242942 

•002087683 

480 

230400 

110592000 

21-9089023 

7-8297353 

•002083333 

481 

231361 

111284641 

21-9317122 

7-8351688 

•002079002 

482 

232324 

111980168 

21-9544984 

7-8405949 

•002074689 

483 

233289 

112678587 

21-9772610 

7-8460134 

•002070393 

484 

234256 

113379904 

22-0000000 

7-8514244 

•00206C116 

485 

235225 

114084125 

22-0227155 

7-8568281 

•002061856 

486 

23C196 

114791256 

22-0454077 

7-8622242 

•002057613 

487 

237169 

115501303 

22-0680765 

7-8676130 

•002053388 

483 

238144 

116214272 

22-0907220 

7-8729944 

•002049180 

489 

239121 

116930169 

22-1133444 

7-8783684 

•002044990 

490 

240100 

117649000 

22-1359436 

7-8837352 

•002040816 

491 

241081 

118370771 

22-1585198 

7-8890946 

•0020366GO 

492 

242064 

119095488 

22-1810730 

7-89444C8 

•002032520 

493 

243049 

119823157 

22-2036033 

7-8997917 

•002028398 

494 

244036 

120553784 

22-2261108 

7-9051294 

•002024291 

495 

245025 

121287375 

22-2485955 

7-9104599 

•002020202 

496 

246016 

122023936 

22-2710575 

7-9157832 

•00201C129 

497 

247009 

122763473 

22-2934908 

7-9210994 

•002012072 

498 

248004 

123505992 

22-31591C6 

7-9264085 

•002008032 

499 

249001 

124251499 

22-3383079 

7-9317104 

•002004008 

500 

250000 

125000000 

22-3606798 

7-9370053 

•002000000 

501 

251001 

125751501 

22-3830293 

7-9422931 

•00199C008 

502 

252004 

126506008 

22-4053505 

7-9475739 

•001992082 

503 

253009  127263527 

22-4276615 

7-9528477 

•0019SS072 

504 

254016  128024064 

22-4499443 

7-9581144 

•001984127 

505 

255025  128787625 

22-4722051 

7-963C743 

•001980198 

506 

256036  129554216 

2°-4944438 

7-9GS6271 

•001976285 

507 

257049  130323843 

22-5166605 

7-9738731 

•001972387 

503 

258064  131096512 

22-5388553 

7-9791122 

•001C68504 

509 

259081  131972229 

22-5610283 

7-9843444 

•001964637 

510 

260100!  132651000 

22-5831796 

7-9895697 

•0019C07S4 

511 

261121  133432831 

22-6053091 

7-99478S3 

•001956947 

512 

262144 

134217728 

22-6274170 

8-0000000 

•001953125 

513 

263169 

135005697 

22-6495033 

8-0052049 

•001949518 

514 

264196  i  135796744 

22-6715681 

8-0104032 

•001945525 

515 

265225  136590875 

22-6936114 

8-0155946 

•001941748 

516 

266256  137388096 

22-7156334 

8-0207794 

•001937t)84 

517 

267289  ,  138188413 

22-7376341 

8-0259574 

•001934236 

518 

268324 

138991832 

22-7596134 

8-0311287 

•001930502 

519 

269361 

139798359 

22-7815715 

8-0362935 

•001926782 

520  I 

270400 

140G08000 

22-8035085  , 

8-0414515 

•001923077 

TABLE  OP  SQUARES,  CBEES,  SQUARE  AND  CUBE  HOOTS. 


Number. 

Squares. 

Cubes. 

VKootg. 

4/  Roots. 

Reciprocals. 

521 

271411 

141420761 

22-8254244 

8-0466030 

•001919386 

522 

272484 

142236648 

22-8473193 

8-0517479 

•001915700 

523 

273529 

143055667 

22-8691933 

8-0568862 

•001912046 

521 

274576 

143877824 

22-8910463 

8-0620180 

•001908397 

525 

275625 

144703125 

22-9128785 

8-0671432 

•001904762 

526 

276676 

145531576 

22-9346899 

8-0722620 

•001901141 

527 

277729 

146363183 

22-9564806 

8-0773743 

•001897533 

523 

278784 

147197952 

22-9782506 

8-0824800 

•001893939 

529 

279841 

148035889 

23-0000000 

8-08/5794 

•001890359 

530 

280900 

148877001 

23-0217289 

8-0926723 

•001886792 

531 

281961 

149721291 

23-0434372 

8-0977589 

•001883239 

532 

283024 

150568768 

23-0651252 

8-1028390 

•001879699 

533 

284089 

151419437 

23-0867928 

8-1079128 

•001876173 

534 

285156 

152273304 

23-1084400 

8-1129803 

•001872659 

535 

286225 

153130375 

23-1300670 

8-1180414 

•001869159 

536 

287296 

153990656 

23-1516738 

8-1230962 

•001865672 

537 

288369 

154854153 

23-1732605 

8-1281447 

•001862197 

538 

289444 

155720872 

23-1948270 

8-1331870 

•001858736 

539 

290521 

156590819 

23-2163735 

8-1382230 

•001855288 

540 

291600 

157464000 

23-2379001 

8-1432529 

•001851852 

541 

292681 

158340421 

23-2594067 

8-1482765 

•001848429 

542 

293764 

159220088 

23-2808935 

8-1532939 

•001845018 

543 

294849 

160103007 

23-3023604 

8-1583051 

•001841621 

544 

295936 

160989184 

23-3238076 

8-1633102 

•001838235 

545 

297025 

161878625 

23-3452351 

8-1683092 

•001834862 

546 

298116 

162771336 

23-3666429 

8-1733020 

•001831502 

547 

299209 

163667323 

23-3880311 

8-1782888 

•001828154 

543 

300304 

164566592 

23-4093998 

8-1832695 

•001824818 

549 

301401 

165469149 

23-4307490 

8-1882441 

•001821494 

550 

302500 

166375000 

23-4520788 

8-1932127 

•001818182 

551 

303601 

167284151 

23-4733892 

8-1981753 

•001814882 

552 

304704 

168196608 

23-4946802 

8-2031319 

•001811594 

553 

305809 

169112377 

23-5154)520 

8-2080825 

•001808318 

554 

306916 

170031464 

23-5372046 

8-2130271 

•001805054 

555 

308025 

170953875 

23-5584380 

8-2179657 

•001801802 

556 

309136 

171879616 

23-5796522 

8-2228985 

•001798561 

557 

310249 

172808693 

23-6008474 

8-2278254 

•001795332 

553 

311364 

173741112 

23-6220236 

8-2327463 

•001792115 

559 

312481 

174676879 

23-6431808 

8-2376614 

•001788909 

5GO 

313600 

175616000 

23-6643191 

8-2425706 

•001785714 

5G1 

314721 

176558481 

23-6854386 

8-2474740 

•001782531 

5G2 

315844 

177504328 

23-7065392 

8-2523715 

•001779359 

5G3 

316969 

178453547 

23-7276210 

8-2572635 

•001776199 

564 

318096 

179406144 

23-7486842 

8-2621492 

•001773050 

565 

319225 

180362125 

23-7697286 

8-2670294 

•001769912 

566 

320356 

181321496 

23-7907545 

8-2719039 

•001766784 

567 

321489 

182284263 

23-8117618 

8-2767726 

•001763668 

563 

322624 

183250432 

23-8327506 

8-2816255 

•001760563 

569 

323761 

184220009 

23-8537209 

8-2864928 

•001757469 

570 

324900 

185193000 

23-8746728 

8-2913444 

•001754386 

571 

326041 

186169411 

23-8956063 

8-2961903 

•001751313 

572 

327184 

187149248 

23-9165215 

8-3010304 

•001748251 

TABLE  OP  SQUARES,  CUBES,  SQUARE  AND  CUBE  ROOTS. 


Number. 

Squares. 

Cubes. 

<J  Roots. 

fy  Root*. 

Reciprocals. 

573 

328329 

188132517 

23-9374184 

8-3058651 

•001745201 

574 

329476 

189119224 

23-9582971 

8-3106941 

•001742160 

575 

330625 

190109375 

23-9791576 

8-3155175 

•001739130 

576 

331776 

191102976 

24-0000000 

8-3203353 

•001736111 

577 

332927 

192100033 

24-0208243 

8-3251475 

•001733102 

578 

334084 

193100552 

24-0416306 

8-3299542 

•001730104 

579 

335241 

194104539 

24-0624188 

8-3347553 

•001727116 

580 

336400 

195112000 

24-0831891 

8-3395509 

•001724138 

581 

337561 

196122941 

24-1039416 

8-3443410 

•001721170 

582 

33S724 

197137368 

24-1246762 

8-3491256 

•001718213 

583 

339889 

198155287 

24-1453929 

8-3539047 

•001715266 

584 

341056 

199176704 

24-1660919 

8-3586784 

•001712329 

585 

342225 

200201625 

24-1867732 

8-3634466 

•001709402 

586 

343396 

201230056 

24-2074369 

8-3682095 

•001706485 

587 

344569 

202262003 

24-2280829 

8-3729668 

•001703578 

588 

345744 

203297472 

24-2487113 

8-3777188 

•001700680 

689 

346921 

204336469 

24-2693222 

8-3824653 

•001697793 

590 

348100 

205379000 

24-2899156 

8-3872065 

•001C94915 

591 

349281 

206425071 

24-3104996 

8-3919428 

•001692047 

592 

350464 

207474688 

24-3310501 

8-3966729 

•001689189 

593 

351649 

208527857 

24-3515913 

8-4013981 

•001686341 

594 

352836 

209584584 

24-3721152 

8-4061180 

•001683502; 

595 

354025 

210644875 

24-3926218 

8-4108326 

•001680672 

596 

355216 

211708736 

24-4131112 

8-4155419 

•001677852 

597 

356409 

212776173 

24-4335834 

8-4202460 

•001675042 

598 

357604 

213847192 

24-4540385 

8-4249448 

•001672241 

599 

358801 

214921799 

24-4744765 

8-4296383 

•001669449 

600 

360000 

216000000 

24-4948974 

8-4343267 

•001666667 

601 

361201 

217081801 

24-5153013 

8-4390098 

•001663894" 

602 

362404 

218167208 

24-5356883 

8-4436877 

•001661130 

603 

363609 

219256227 

24-5560583 

8-4483605 

•00165837& 

604 

364816 

220348864 

24-5764115 

8-4530281 

•001655629 

605 

366025 

221445125 

24-5967478 

8-4576906 

•001652893 

606 

367236 

222545016 

24-6170673 

8-4623479 

•001650165 

607 

368449 

223648543 

24-6373700 

8-4670001 

•001647446 

608 

369664 

224755712 

24-6576560 

8-4716471 

•001644737 

609 

370881 

225866529 

24-6779254 

8-4762892 

•001642036 

610 

372100 

226981000 

24-6981781 

8-4809261 

•001639344 

611 

373321 

228099131 

24-7184142 

8-4855579 

•001626661 

612 

374544 

229220928 

24-7386338 

8-4901848 

•001633987 

613 

375769 

230346397 

24-7588368 

8-4948065 

•001631321 

614 

376996 

231475544 

24-7790234 

8-4994233 

•001628664 

615 

378225 

232608375 

24-7991935 

8-5040350 

•001626016 

616 
617 

379456 
380689 

233744896  24-8193473 
234885113  '  24-8394847 

8-5086417 
8-5132435 

•001623,477 
•001620746 

618 

381924 

236029032 

24-8596058 

8-5178403 

•001618123 

619 

383161 

237176659 

24-8797106 

8-5224331 

•001615509 

620 

384400 

238328000 

24-8997992 

8-5270189 

•001612903 

621 

385641 

239483061 

24-9198716 

8-5316009 

•001610306 

622 

386884 

240641848 

24-9399278 

8-5361780 

•001607717 

623 

388129 

241804367 

24-9599679 

8-5407501 

•001605136 

624 

3893761242970624 

24-9799920  • 

8-5453173 

001602564 

TABLE  OP  SQUARES,  CUBES,  SQUARE  AND  CUBE  BOOTS. 


Number. 

Squared. 

Cubes. 

^/  Boots. 

•tyKoots. 

Reciprocals. 

C25 

390625 

244140625 

25-0000000 

8-5498797 

•001600000 

626 

391876 

245134376 

25-0199920 

8-5544372 

•001597444 

627 

393129 

246491883 

25-0399681 

8-5589899 

•001594896 

628 

394384  247673152 

25-0599282 

8-5635377 

•001592357 

629 

395641  24S858189 

25-0798724 

8-5680807 

•001589825 

630 

396900  '250047000 

25-0998008 

8-5726189 

•001587302 

631 

39816H251239591 

25-1197134 

8-5771523 

•001584786 

632 

399424  252435968 

25-1396102 

8-5816809 

•001582278 

633 

400689  253636137 

25-1594913 

.  8-5862247 

•001579779 

634 

4019561254840104 

25-1793566 

8-5907238 

•001577287 

635 

403225  256047875 

25-1992063 

8-5952380 

•001574803 

636 

404496  '257259456 

25-2190404 

8-5997476 

•001572327 

637 

405769  238474853 

25-2388589 

8-6042525 

•001569859 

638 

407044  259694072 

25-2586619 

8-6087526 

•001567398 

639 

408321  260917119 

25-2784493 

8-6132480 

•001564945 

640 

409600  i  262144000 

25-2982213 

8-6177388 

•001562500 

641 

410881 

263374721 

25-3179778 

8-6222248 

•001560062 

642 

412164 

264609288 

25-3377189 

8-6267063 

•001557632 

643 

413449 

265847707 

25-3574447 

8-6311830 

•001555210 

644 

414736 

267089984 

25-3771551 

8-6356551 

•001552795 

645 

416125 

268336125 

25-3968502 

8-6401226 

•001550388 

646 

417316 

269585136 

25-4165302 

8-6445855 

•001547988 

647 

4186091270840023 

25-4361947 

8-6490437 

•001545595 

648 

419904 

272097792 

25-4558441 

8-6534974 

•001543210 

649 

421201 

273359449 

25-4754784 

8-6579465 

•001540832 

650 

422500 

274625000 

25-4950976 

8-6623911 

•001538462 

651 

423801 

275894451 

25-5147013 

8-6668310 

•001530098 

652 

425104 

277167808 

25-5342907 

8-6712665 

•001533742 

653 

426409 

278445077 

25-5538647 

8-6756974 

•001531394 

654 

427716 

279726264 

25-5734237 

8-6801237 

•001529052 

655 

429025 

281011375 

25-5929678 

8-6845456 

•001526718 

656 

430336 

282300416 

25-6124969 

8-6889630 

•001524390 

657 

431639 

283593393 

25-6320112 

8-6933759 

•001522070 

658 

432964 

284890312 

25-6515107 

8-6977843 

•001519751 

659 

434281 

286191179 

25-6709953 

8-7021882 

•001517451 

660 

435600 

287496000 

25-6904652 

8-7065877 

•001515152 

661 

436921 

288804781 

25.7099203 

8-7109827 

•001512859 

662 

438244 

290117528 

25-7293607 

8-7153734 

•001510574 

663 

439569 

291434247 

25-7487864 

8-7197596 

•001508296 

6f>4 

440896 

292754944 

25-7681975 

8-7241414 

•001506024 

665 

442225 

294079625 

25-7875939 

8-7285187 

•001503759 

666 

443556 

295408296 

25-8069758 

8-7328918 

•001501502 

667 

444899 

296740963 

25-8263431 

8-7372604 

•001499250 

668 

446224 

298077632 

25-8456960 

8-7416246 

•001497006 

669 

447561 

299418309 

25-8650343 

8-7459846 

•001494768 

ero 

448900 

300763000 

25-8843582 

8-7503401 

•001492537 

671 

450241 

302111711 

25-9036677 

8-7546913 

•001490313 

672 

451584 

303464448 

25-9229628 

8-7590383 

•001488095 

673 

452929 

304821217 

25-9422435 

8-7633809 

•001485884 

674 

454276 

306182024 

25-9615100 

8-7C771S2 

•001483680 

675 

455625 

307546875 

25-9807621 

8-7720532 

•001481481 

676 

456976 

308915776 

26-0000000 

8-7763830 

•001479290 

TABLE  OP  SQUARES,  CUBES,  SQUARE  AM>  CUBB  ROOTS. 


Number. 

Squares. 

Cubes. 

\f  Boots. 

%  Roots. 

Reciprocal 

677 

458329 

310288733 

26-0192237 

8-7807084 

•0014771 

C7S 

459684 

311665752 

26-0384331 

8-7850296 

•0014749 

679 

461041 

313046839 

26-0576284 

8-7893406 

•0014727 

680 

4G2400 

314432000 

26-0768096 

8-7936593 

•0014705 

651 

4G3761 

315821241 

26-0959767 

8-7979679 

•0014684 

CS2 

465124 

317214568 

26-1151297 

8-8022721 

•0014662 

683 

466489 

318611987 

26-1342687 

8-8065722 

•0014641 

6S4 

467856 

320013504 

26-1533937 

8-810S6S1 

•0014619 

685 

469225 

321419125 

26-1725047 

8-8151598 

•0014598 

6S6 

470596 

322828856 

26-1916017 

8-8194474 

•0014577 

637 

471969 

324242703 

26-2106848 

8-8237307 

•0014556 

688 

473344 

325660672 

26-2297541 

8-8280099 

•0014534 

6S9 

474721 

327082769 

26-2488095 

8-8322850 

•0014513 

690 

476100 

328509000 

26-2678511 

8-8365559 

•0014492 

691 

477481 

329939371 

26-2868789 

8-8408227 

•0014471 

692 

478864 

331373888 

26-3058929 

8-8450854 

•0014450 

693 

4S0249 

332812557 

26-3248932 

8-8493440 

•0014430 

694 

481636 

334255384 

26-3438797 

8-8535985 

•0014409 

C95 

483025 

335702375 

26-3628527 

8-8578489 

•0014388 

696 

484416 

337153536 

26-3818119 

8-8620952 

•0014367 

697 

485809 

338608873 

26-4007576 

8-8663375 

•0014347 

693 

487204 

340068392 

26-4196896 

8-8705757 

•0014326 

609 

488601 

341532099 

26-4386081 

8-8748099 

•0014306 

700 

490000 

343000000 

26-4575131 

8-8790400 

•0014285 

701 

491401 

344472101 

26-4764046 

8-8832661 

•0014265 

702 

492804 

345948408 

26-4952826 

8-8874882 

•0014245 

703 

494209 

347428927 

26-5141472 

8-8917063 

•0014224 

704 

495C16 

348913664 

26-5329983 

8-8959204 

•0014204 

705 

497025 

350402625 

26-5518361 

8-9001304 

•0014184 

706 

498436 

351895816 

26-5706605 

8-9043366 

•0014164 

707 

499849 

353393243 

26-5894716 

8-90853S7 

•0014144 

708 

501264 

354894912 

26-6082694 

8-9127369 

•0014124 

709 

502681 

356400829 

26-6270539 

8-9169311 

•0014104 

710 

504100 

357911000 

26-6458252 

8-9211214 

•0014084 

711 

505521 

359425431 

26-6645833 

8-9253078 

•0014064 

712 

506944 

360944128 

26-6833281 

8-9294902 

•0014044 

ris 

508369 

362467097 

26-7020598 

8-9336687 

•0014025 

714 

509796 

363994344 

26-7207784 

8-9378433 

•0014005 

715 

511225 

365525875 

26-7394839 

8-9420140 

•0013986 

710 

512656 

367061696 

26-7581763 

8-9461809 

•0013966 

717 

514089 

368601813 

26-7768557 

8-9503438 

•0013947 

718 

515524 

370146232 

26-7955220 

8-9545029 

•0013927 

719 

516961 

371694959 

26-8141754 

8-9586581 

•0013908 

720 

518400 

373248000 

26-8328157 

8-9628095 

•0013888 

721 

519841 

374805361 

26-8514432 

8-9669570 

•0013869 

722 

521284 

376367048 

26-8700577 

8-9711007 

•0013850 

723 

522729 

377933067 

26-8886593 

8-9752406 

•0013531 

724 

524176  379503424  26-9072481 

8-9793766 

•001381? 

725 

525625 

381078125  26-9258240 

8-9835089 

•0013793 

726 

527076 

382657176 

26-9443872 

8-9876373 

•0013774 

,727 

528529 

384240583 

26-9629375 

8-9917620 

•0013755 

923 

629984 

385828352 

26-9814751 

8-9958899 

•0013756 

TABLE  OP  SQUARES,  CUBES,  SQUARE  AND  CUBE  ROOTS. 


amber. 

Squares. 

Cubes. 

V/  Roots. 

j/  Roots. 

Reciprocz 

729 

531441 

387420489 

27-0000000 

9*0000000 

-001371 

730 

532900 

389017000 

27-0185122 

9*0041134 

•001369 

731 

534361 

390617891 

27-0370117 

9*0082229 

•001367 

732 

535824 

392223168 

27*0554985 

9*0123288 

•001366 

733 

537289 

393832837 

27-  '.'739727 

9*0164309 

•001364 

734 

538756 

395446904 

27-0924344 

9-0205293 

•001362 

735 

540225 

397065375 

27*1108834 

9-0246239 

•001360 

736 

541696 

398688256 

27-1293199 

9-0287149 

•001358 

737 

543169 

400315553 

27-1477149 

9-0328021 

•001356 

738 

544644 

401947272 

27-1661554 

9-0368857 

•001355 

739 

546121 

403583419 

27-1845544 

9-0409655 

•001353 

740 

547600 

405224000 

27-2029140 

9-0450419 

•001351 

741 

549801 

406869021 

27-2213152 

9*0491142 

•001349 

V42 

550564 

408518488 

27-2396769 

9*0531831 

•001347 

743 

552049 

410172407 

27-2580263 

9*0572482 

•001345 

744 

553536 

41183P784 

27*2763634 

90613098 

•001344 

745 

555025 

413493625 

27*2946881 

9*0653677 

•001342 

746 

556516 

415160936 

27*3130006 

9*0694220 

•001340 

«T47 

558009 

416832723 

27*3313007 

9*0734726 

•001338 

£48 

559504 

418508992 

27*3495887 

9*0775197 

•001336 

749 

561001 

420189749 

27-3678644 

9*0815631 

-001335 

750 

562500 

421875000 

27*3861279 

9*0856030 

•001333 

751 

5640011423564751 

27-4043792 

9*0896352 

•001331 

752 

565504 

425259008 

27*4226184 

9-0936719 

•001329 

753 

567009 

426957777 

27*4408455 

9-0977010 

•001328 

754 

568516 

428661064 

27*4590604 

9-1017265 

•001326 

755 

570025 

430368875 

27*4772633 

9-1057485 

•001324 

756 

571536 

432081216 

27*4954542 

9*1097669 

•001322 

757 

573049 

433798093 

27*5136330 

9-1137818 

•001321 

758 

574564 

435519512 

27*5317998 

9-1177931 

•001319 

759 

576081 

437245479 

27*5499546 

9-1218010 

-001317 

760 

577600 

438976000 

27-5680975 

9*1258053 

•001315 

761 

579121 

440711081 

27-5862284 

9*1298061 

•001314 

762 

580644 

442450728 

27-6043475 

9-1338034 

•001312 

763 

582169 

444194947 

27-6224546 

9-1377971 

•001310 

764 

583696 

445943744 

27-6405499 

9-1417874 

•001308 

765 

585225 

447697125 

27*6586334 

9-1457742 

•001307 

766 

586756 

449455096 

27-6767050 

9*1497576 

•001305 

767 

588289 

4512176631  27-6947648 

9-1537375 

•001303 

768 

589824 

452984832  !  27-7128129 

9-1577139 

•001302 

769 

591361 

454756609'  27-7308492 

9-1616869 

•001300 

770 

592900 

456533000  ;  27*7488739 

9-1656565 

•001298 

771 

594441 

45831401  Ij  27-7668868 

9-1696225 

•001297 

772 

595984 

4P0099648  27-7848880 

9-1735852 

•001295 

773 

597529 

461889917 

27-8028775 

9-1775445 

•001293 

774 

599C76 

463684824 

27-8208555 

9-1815003 

•001291 

775 

600625 

465484375 

27-3388218 

9-1854527 

•00129C 

776 

602176 

467288576 

27-8567766 

9-1894018 

•001288 

777 

603729 

469097433 

27-8747197 

9-1933474 

•001287 

778 

605284 

470910952 

27-8926514 

9-1972897 

•001285 

779 

606841 

472729139 

27-9105715 

9*2012286 

•001283 

780 

60*400 

474552000 

27*9284801 

9*2051641 

•001282 

TABLE  OP  SQUARES,  CUBES,  SQUARE  ANT>  CUBE  ROOTS. 


Number,  j  Squares. 

Cubes. 

^  Roots. 

^Koota. 

Reciprocals. 

781 

609061 

476379541 

27-9463772 

9-2090962 

•00128041 

782 

611524 

478211768 

27-9642629 

9-2130250 

•00127877 

783 

613089 

480048687 

27-9821372 

9-2169505 

•00127713 

784 

614656 

481890304 

28-0000000 

9-2208726 

•00127551 

785 

616225 

i  483736625 

28-0178515 

9-2247914 

•00127388 

786 

617796 

485587656 

28-0356915 

9-2287068 

•00127226 

787 

619369 

487443403 

28-053^203 

9-2326189 

•00127064 

788 

620944 

489303872 

28-0713377 

9-2365277 

•00126903 

789 

622521 

491169069 

28-0891438 

9-2404333 

•00126742 

790 

624100 

493039000 

28-1069386 

9-2443355 

•00126582 

791 

625681 

494913671 

28-1247222 

9-2482344 

•00126422 

792 

627264 

496793088 

28-1424946 

9-2521300 

•001262B2 

793 

628849 

498677257 

28-1602557 

9-2560224 

•001261D3* 

794 

630436 

500566184 

28-1780056 

9-2599114 

•00125944 

795 

632025 

502459875 

28-1957444 

9-2637973 

•00125786- 

796 

633616 

504358336 

28-2134720 

9-2676798 

•OC125628 

797 

635209 

506261573 

28-2311884 

9-2715592 

•CG125470 

798 

636804 

508169592 

28-2488938 

9-2754352 

•OCI25313, 

799 

638401 

510082399 

28-2665881 

9-2793081 

•00125136' 

800 

640000 

512000000 

28-2842712 

9-2831777 

•001250001 

801 

641601 

513922401 

28-3019434 

9-2870444 

•00124843* 

802 

643204 

515849608 

28-3196045 

9-2909072 

•00124688; 

803 

644809 

517781627 

28-3372546 

9-2947671 

•001245331 

804 

646416 

519718464 

28-3548938  !  9-2986239 

•001243781 

805 

648025 

521660125 

28-3725219 

9-3024775 

•00124223( 

806 

649636 

523606616 

28-3901391 

9-3063278 

•00124069* 

807 

651249 

525557943 

28-4077454 

9-3101750 

•00123915' 

808 

652864 

527514112 

28-4253408 

9-3140190 

•00123762^ 

809 

654481 

529475129 

28-4429253 

9-3178599 

•00123609^ 

810 

656100 

531441000 

28-4604989 

9-3216975 

•00123456* 

811 

657721 

533411731 

28-4780617 

9-3255320 

•00123304* 

812 

659344 

535387328 

28-4956137 

9-3293634 

•00123152; 

813 

660969 

537357797 

28-5131549 

9-3331916 

•0012'30015 

814 

662596 

539353144 

28-5306852 

9-3370167 

•00122850J 

815 

664225 

541343375 

28-5482048 

9-3408386 

/001226994 

816 

665856 

543338496 

28-5657137 

9-3446575 

•00122549$ 

817 

667489 

545338513 

28-5832119 

9-3484731 

•00122399C 

818 

669124 

547343432 

28-6006993 

9-3522857 

•001222494 

819 

670761 

549353259 

28-6181760 

93560952 

•001221001 

820 

672400 

5513680GO 

28-6356421 

0-3599016 

•001219512 

821 

674041 

553387661 

28-6530976 

9-3637049 

•001218027 

822 

675684 

555412248 

28-6705424 

9-3675051 

•001216545 

823 

677329 

557441767 

28-6879716 

9-3713022 

•007215067 

824 

678976 

559476224 

28-7054002 

9-3750963 

•001213592 

825 

680625 

561515625 

28-7228132 

9-3788873 

•001212121 

826 

682276 

563559976 

28  7402157 

9-3826752 

•001210654 

827 

683929 

565609283 

28-7576077 

9-3864600 

•00120919C 

828 

685584 

567663552 

28-7749891 

9-3902419 

•00120772S 

829 

687241 

569722789 

28-7923601 

9-3940206 

•001206273 

830 

688900 

571787000 

28-8097206 

9-3977964 

•001204819 

831 

690561 

573856191 

28-8270706 

9-4015691 

•001203369 

832 

692224 

575930368 

28-8444102 

9-4053387 

•001201923 

TAJBUS  OF  SQUARES,  CUBES,  SQUARE  AITO  CUBE  ROOTS. 


Number. 

Squares. 

Cubes. 

v/  Roots. 

ff  Roots. 

Reciprocals 

833 

693889 

578009537 

28-86173.94 

9-4091054 

•001200480 

834 

695556 

5S0093704 

28-8790582 

9-412SC90 

•001199041 

835 

697225 

582182875 

28-8963666 

9-4166297 

•001197605 

836 

698896 

584277056 

28-9136646 

9-4203873 

•001196172 

837 

700569 

586376253 

28-9309523 

9-4241420 

•001194743 

833 

702244 

588480472 

23-9482297 

9-4278936 

•001193317 

839 

703921 

590589719 

28-9654967 

9-4316423 

•001191895 

8-10 

705SOO 

592704000 

28-9827535 

9-4353800 

•001190476 

841 

707281 

594823321 

29-0000000 

9-4391307 

•001189061 

812 

708964 

5969476S8 

29-0172363 

9-4428704 

•001187648 

813 

710649 

599077107 

29-0344623 

9-4466072 

•001186240 

844 

712336 

601211584 

29-0516781 

9-4503410 

•001184834 

845 

714025 

603351125 

29-0688837 

9-4540719 

•001183432 

846 

715716 

605495736 

29-0860791 

9-4577999 

•001182033 

847 

717409 

607645423 

29-1032644 

9-4615249 

•001180638 

848 

719104 

609300192 

29-1204396 

9-4652470 

•001179245 

849 

720801 

611960049 

29-1376046 

9-4689661 

•001177856 

850 

722500 

614125000 

29-1547595 

9-4726824 

•001176471 

851 

724201 

616295051 

29-1719043 

9-4763957 

•001175088 

852 

725904 

618470208 

29-1890390 

9-4801061 

•001173709 

853 

727609 

620650477 

29-2061637 

9-4838136 

•001172333 

854 

729316 

622835864 

29-2232784 

9-4875182 

•001170960 

855 

856 

731025 
732736 

625026375 
627222016 

29-2403830 
29-2574777 

9-4912200 
9-4949188 

•001169591 
•001168224 

857 

734449 

629422793 

29-2745623 

9-4986147 

•001166861 

858 

736164 

631628712 

29-2916370 

9*5023078 

•001165501 

859 

737881 

633839779 

29-3087018 

9-5059980 

•001164144 

860 

739600 

636056000 

29-3257566 

9-5096854 

•001162791 

801 

741321 

638277381 

29-3428015 

9-5133699 

•001161440 

862 

743044 

640503928 

29-3598365 

9-5170515 

•001160093 

863 

744769 

642735647 

29-376S616 

9-5207303 

•001158749 

864 

746496  644972544 

29-3938769 

9-5244063 

•001157407 

865 

748225 

647214625 

29-4108323 

9-5280794 

•001156069 

866 

749956 

649461896 

29-4278779 

9-5317497 

•001154734 

867 

751689 

651714363 

29-4448637 

9-5354172 

•001153403 

868 

753424 

653972032 

29-4618397 

9-5390818 

•001152074 

869 

755161 

656234909 

29-4788059 

9-5427437 

•001150748 

870 

756900 

658503000 

29-4957624 

9-5464027 

•001149425 

871 

758641 

660776311 

29-5127091 

9-5500589 

•001148106 

872 

760384 

663054848 

29-5296461 

9-5537123 

•001146789 

873 

762129  1  665338617  29-5465734 

9-5573630 

•001145475 

874 

763876  667627624  29-5634910 

9-5610108 

•001144165 

875 

765625  669921875  i  29-5803989 

9-5646559 

•001142857 

876 

767376  672221376J  29-5972972 

9-5682782 

•001141553 

877 

769129  674526133 

29-6141858 

9-5719377 

•001140251 

873 

770884  676836152 

29-6310648 

9-5755745 

•001138952 

879 

772641  679151439 

29-6479342 

9-5792085 

•001137656 

880 

774400  681472000 

29-6647939 

9-5828397 

•001136364 

881 

776161  j  683797841 

29-6816442 

9-5864682 

•001135074 

882 

777924 

686128968 

29-6984848 

9-5900937 

•001133787 

883 

779689 

688465387 

29-7153159 

9-5937169 

•001132503 

884 

781456  1690807104 

29-7321375 

9-5973373 

•001131222 

TABLE  OP  SQUARES,  CUBES,  SQUARE  AITD  CUBE  ROOTS. 


Number. 

Squares. 

Cubes. 

V  Roots. 

ty  Roots. 

Reciprocals. 

885 

783225 

693154125 

29-7489496 

9-6009548 

•00112994'! 

886 

784996 

695506456  29*7657521 

9-6045696 

•001128668 

887  - 

W6T69  697864103J  29-7825452 

9-6081817 

•001127396 

S88 

788544 

700227072  ',  29-7993289 

,.9-6117911 

•001126126 

889 

790321 

702595369  29-8161030 

9-6153977 

•001124859 

89S 

792100  i  704969000  :  29-8328678 

9-6190017 

•001123596 

891 

793881  |  707347971  29-8496231 

9-6226030 

•001122334 

892 

795664 

707932288 

29-8663690 

9-6262016 

•001121076 

893 

797449 

712121957 

29-8831056 

9-6297975 

•001119821 

894 

799236 

714516984 

29-8998328 

9-6333907 

•001118568 

895 

801025 

716917375 

29-9165506 

9-6369812 

•001117818 

896 

802816 

719323136 

29-9332591 

9-6405690 

•001116071 

897 

804609 

721734273 

29-9499583 

9-6441542 

•001114827 

898 

806404 

724150792 

29-9666481 

9-6477367 

•001113586 

899 

808201 

726572699 

29-9833287 

9-6513166 

•001112347 

900 

810000 

729000000 

30-0000000 

9-6548933 

•001111111 

901 

811801 

731432701 

30-0166621 

9-6584684 

•001109878 

902 

813604 

733870808 

30-0333148 

9-6620403 

•001108647 

903 

815409 

736314327 

30-0499584 

9-6656096 

•001107420 

904 

817216 

738763264 

30-0665928 

9-6691762 

•001106195 

905 

819025  741217625 

30-0832179 

9-6727403 

•001104972 

906 

820836  743677416 

30-0998339 

9-6763017 

•001103753 

907 

822649 

746142643 

30-1164407 

9-6798604 

•001102536 

908 

824464 

748613312 

20-1330383 

9-6834166 

•001101322 

909 

826281 

751089429 

30-1496269 

9-6869701 

•001100110 

910 

828100 

753571000 

30-1662063 

9-6905211 

•001098901 

911 

829921 

756058031 

30-1827765 

9-6940694 

•001097695 

912 

831744 

758550825 

30-1993377 

9-6976151 

•001096491 

913 

83356^ 

761048497 

30-2158899 

9-7011583 

•001095290 

914 

831)396 

763551944 

30-2324329 

9-7046989 

•001094092 

915 

837225 

766060875 

30-2489669 

9-7082369 

•001092896 

916 

839056 

768575296 

30-2654919 

9-7117723 

•001091703 

917 

840889 

771095213 

30-2820079 

9-7153051 

•001090513 

918 

842724 

773620632 

30-2985148 

9-7188354 

•001089325 

919 

844561 

776151559 

30-3150128 

9-7223631 

•001088139 

920 

846400 

778688000 

30-3315018 

9-7258883 

•001086957 

921 

848241 

781229961 

30-3479818 

9.7294109 

•001085776 

922 

850084 

783777448 

30-3644529 

9-7329309 

•001084599 

923 

851929 

786330467 

30-3809151 

9-7364484 

•001083423 

924 

853776 

788889024 

30-3973683 

9-7399634 

•001082251 

925 

855625 

791453125 

30-4138127 

9-7434758 

•001081081 

926 

857476 

794022776 

30-4302481 

9-7469857 

•001079914 

927 

859329 

796^97983 

30-4466747 

9-7504930 

•001078749 

928 

861184 

799178752 

30-4630924 

9-7539979 

•001077586 

929 

863041 

801765089 

30-4795013 

9-7575002 

•001076426 

930 

864900 

804357000 

30-4959014 

9-7610001 

•001075269 

931 

866761 

806954491 

30-5122926 

9-7644974 

•001074114 

932 

868624 

809557568 

30-5286750 

9-7679922 

•001072961 

933 

870489 

812166237 

30-5450487 

9-7714845 

-001071811 

934 

872356 

814780504 

30-5614136 

9-7749743 

•001070664 

935 

874225 

817400375 

30-5777697 

9-7784616 

•001069519 

936 

876096 

820025856 

30-5941171 

9-7819466 

•001068376 

APPENDIX. 


Haskins'  Differential. — In  this  form  of  galvano- 
meter no  rheostat  is  used.  Two  coils  of  equal  power 
are  placed,  one  above,  and  the  other  below,  the  needle. 

The  upper  coil  is  raised  and  lowered  by  a  screw. 
Attached  to  the  top  of  the  upper  coil  is  a  segment 
of  a  circle,  on  which  rests  a  lever  with  a  knife-edge 
agate  terminal  to  prevent  wearing.  On  the  top  of 
the  instrument-box  is  a  circular  dial,  divided  into  five 
ohm  graduations.  A  hand,  bearing  a  vernier  on  its 
free  extremity,  is  moved  by  the  upper  coil  through 
the  medium  of  the  segment  and  the  lever  above  de- 
scribed. 

•The  resistance  to  be  measured  is  inserted  in  the 
circuit  of  the  lower,  stationary  coil.  When  the  key 
is  closed  the  upper  coil  gets  more  current  than  the 
lower,  and  deflects  the  needle.  This  coil  is  now 
raised  until,  owing  to  its  greater  distance  from  the 
needle,  its  effect  is  the  same  as  the  lower  coil,  and 
the  needle  returns  to  zero.  The  hand  on  the  dial 
now  gives  the  exact  resistance  in  ohms  reading  to 
half  an  ohm.  In  this  instrument  it  will  be  seen  that 
distance,  instead  of  artificial  resistance,  is  used  to  ob- 
tain a  balance. 

Galvanometers  are  made  upon  this  plan  with  a 
capacity  of  2,000  ohms  measurement,  but  a  few 
inches  in  size,  which  may  readily  be  carried  MI  a 
coat-pocket. 


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CAIN  (Prof.  WM .)    A  Practical  Treatise  on  Voussoir  and  Solid 

and  Braced  Arches.    i6mo,  cloth  extra $i  75 

CALDWELL  (Prof.  GEO.  C.1  and  BRENEMAN  (Prof.  A.  A.) 
Manual  of  Introductory  Chemical  Practice,  for  the  use  of 
Students  in  Colleges  and  Normal  and  High  Schools.  Third 
edicion,  revised  and  corrected.  8vo,  cloth,  illustrated.  New 
and  enlarged  edition I  50 

CAMPIN  (FRANCIS).    On  the  Construction  oflron  Roofs.  8vo, 

with  plates,  cloth  . , 2  oo 

CHAUVENET  (Prof.  W.)  New  method  of  correcting  Lunar 
Instances,  and  improved  method  of  finding  the  error  and 
rate  of  a  chronometer,  by  equal  altitudes.  8vo,  cloth 2  oo 

CHURCH  (JOHN  A.)    Notes  of  a  Metallurgical  Journey  in 

Europe.     8vo,  cloth. 2  oo 

CLARK  (D.  KINNEAR,  C.E.)  Fuel:  Its  Combustion  and 
Economy,  consisting  of  Abridgments  of  Treatise  on  the 
Combustion  of  Coal  and  the  Prevention  of  Smoke,  by  C. 
W.  Williams ;  and  the  Economy  of  Fuel,  by  T.  S.  Pri- 
deaux.  With  extensive  additions  on  recent  practice  in  the 
Combustion  and  Economy  of  Fuel :  Coal,  Coke,  Wood, 
Peat,  Petroleum,  etc.  i2tno,  cloth I  50 

A  Manual  of  Rules,  Tables,   and  Data  for  Mechanical 

Engineers.  Eased  on  the  most  recent  investigations.     Illus- 
trated with  numerous  diagrams.     1,012  pages.    8vo,  cloth...  7  50 
Half  morocco 10  oo 

CLARK  (Lt.  LEWIS,  U.  S.  N  )  Theoretical  Navigation  and 
Nautical  Astronomy.  Illustrated  with  41  wood-cuts.  8vo, 
cloth I  50 

CLARKE  (T.  C.)  Description  of  the  Iron  Railway  Bridge  over 
the  Mississippi  River  at  Quincy,  Illinois.  Illustrated  with 
21  lithographed  plans.  4to,  cloth 7  50 

CLEVENGER  (S.  R.)  A  Treatise  on  the  Method  of  Govern- 
ment Surve\ing,as  prescribed  by  the  U  S.  Congress  and 
Commissioner  of  the  General  Land  Office,  with  complete 
Mathematical,  Astronomical,  and  Practical  Instructions  for 
the  use  of  the  United  States  Surveyors  in  the  field.  i6mo, 
morocco  2  50 

COFFIN  (Prof.  J.  H.  C  )  Navigation  and  Nautical  Astrono- 
my. Prepared  for  the  use  of  the  U.  S.  Naval  Academy. 
Sixth  edition.  52  wood-cut  illustrations.  I2mo,  cloth 3  50 

COLBURN   (ZERAH).     The  Gas-Works  of  London.     12010, 

boards 60 

COLLINS  (JAS.  E.)    The  Private  Book  of  Useful  Alloys  and 

Memoranda  for  Goldsmiths,  Jewellers,  etc.    18010,  cloth...,      yt 


4  D.  VAN  NOSTRAND'S  PUBLICATIONS. 

CORNWALL  (Prof.  H.  B.)  Manual  of  Blow  Pipe  Analysis, 
Qualitative  and  Quantitative,  with  a  Complete  System  of 
Descriptive  Mineralogy.  8vo,  cloth,  with  many  illustra- 
tions. N.  Y.,  1882 $2  50 

CRAIG  (B.  F  )  Weights  and  Measures.  An  account  of  the 
Decimal  System,  with  Tables  of  Conversion  for  Commer- 
cial and  Scientitic  Uses.  Square  32mo,  limp  clotJa 50 

CRAIG  (Prof.  TEiQS.)    Elements  of  the  Mathematical  Theory 

of  Fluid  Motion,     i6mo,  cloth I  «5 

DAVIS  (C.  B.)  and  RAE  (F.  B.)  Hand-Book  of  Electrical  Dia- 
grams and  Connections.  Illustrated  with  32  full-page  illus- 
trations. Second  edition.  Oblong  8vo,  cloth  extra 2  oo 

DIEDRICH  (TOHN).  The  Theory  of  Strains  :  a  Compendium 
torthe  Calculation  and  Construction  of  Bridges,  Roofs,  and 
Cranes  Illustrated  by  numerous  plates  and  diagrams. 
8vo,idoth 500 

DIXON  /D.  B.)  The  Machinist's  and  Steam-Engineer's  Prac- 
tical Calculator.  A  Compilation  of  useful  Rules,  and  Prob- 
lems Arithmetically  Solved,  together  with  General  Informa- 
tion applicable  to  Shop-Tools,  Mili-Gearing,  Pulleys  and 
Shafts,  Steam-Boilers  and  Engines.  Embracing  Valuable 
Tables,  and  Instruction  in  Screw-cutting,  Valve  and  Link 
Motion,  •etc.  i6mo,  full  morocco,  pocket  form  .  ..(In  press) 

DODD  (GEO.)  Dictionary  of  Manufactures,  Mining,  Ma- 
chinery, and  the  Industrial  Arts .  12010,  cloth i  50 

DOUGLASS  (Prof  S.  H.)  and  PRESCOTT  (Prof.  A.  B.)  Qual- 
itative Chemical  Analysis.  A  Guide  in  the  Practical  Study 
of  Chemistry,  and  in  the  Work  of  Analysis.  Third  edition. 
8vo,  cloth 3  50 

DUBOIS  (A.  .T.)    The  New  Method  of  Graphical  Statics.  With 

60  illustrations.    8vo,  cloth I  50 

EASSIE  (P.  B.)  Wood  and  its  Uses.  A  Handbook  for  the  use 
of  Contractors,  Builders,  Architects,  Engineers,  and  Tim- 
ber Merchants.  Upwards  of  230  illustrations.  8vo,  cloth.  150 

EDDY  (Prof.  H.  T.)  Researches  in  Graphical  Statics,  embrac- 
ing New  Constructions  in  Graphical  Statics,  a  New  General 
Method  in  Graphical  Statics,  and  the  Theory  of  Internal 
Stress  in  Graphical  Statics.  8vo,  cloth I  50 

ELIOT  (Prof.  C.  W ..)  and  STORER  (Prof.  F.  H.)  A  Compen- 
dious Manual  of  Qualitative  Chemical  Analysis.  Revised 
with  the  co-operation  ox  the  authors.  By  Prof.  William  R. 
Nichols.  Illustrated.  i2mo,  cloth 150 

ELLIOT  (Maj.  GEO.  H.,  U.  S.  E.)  European  Light-House 
Systems.  Being  a  Report  of  a  Tour  ol  Inspection  made  in 
1873.  51  engravings  and  21  wood-cuts.  8vuj  cloth 5  oo 


D.  VAN  NOSTRAND'S  PUBLICATIONS.  5 

ENGINEERING  FACTS  AND  FIGURES.  An  Annual 
Register  of  Progress  in  Mechanical  Engineering  and  Con- 
struction for  the  years  1803-6^1-65-66-67-6^  Fully  illus- 
trated. 6  vols.  i8mo,  cloth  (each  volume  sold  separately), 
per  vol 82  5° 

FANNING  (J   T.)     A  Practical  Treatise  of  Water-Supply  En- 

fineering.     Relating  to  the  Hydrology,  Hydrod>namics,  and 
radical  Construction  of  Water-Works  in  North  America. 
Third   edition.      With   numerous    tables  and   180  illustra- 
tions.   650  pages.    8vo,  cloth 5  op 

FISKE  (BRADLEY  A.,  U.  S.  N.)    Electricity  in  Theory  and 

Practice.    8vo,  cioth 25° 

FOSTER  (Gen.  J.  G.,  U.  S.  A  )  Submarine  Blasting  in  Boston 
Harbor,  Massachusetts  Removal  oi  Tower  and  Corwin 
Rocks.  Illustrated  with  seven  plates.  410,  cloth 3  50 

FOYE  (Prof.  J.  C.)  Chemical  Problems.  With  brief  State- 
ments of  the  Principles  involved.  Second  edition,  revised 
and  enlarged.  i6mo,  boards 5° 

FRANCIS  (JAS.  B.,  C  E.)  Lowell  Hydraulic  Experiments : 
Being  a  selection  from  Experiments  on  Hydraulic  Motors, 
on  the  Flow  of  Water  over  Weirs,  in  Open  Canals  of  Uni- 
form Rectangular  Section,  and  through  submerged  Orifices 
and  diverging  Tubes.  Made  Pt  Lowell,  Massachusetts. 
Fourth  edition,  revised  and  enlarged,  with  many  new  ex- 
periments, and  illustrated  with  twenty-three  copperplate 
engravings.  410,  cloth 15  oo 

FREE-KAND  DRAWING.  A  Guide  to  Ornamental  Figure 
and  Landscape  Drawing.  By  an  Art  Student.  i8mo, 
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GILLMORE  (Gen.  Q.  A.)  Treatise  on  Limes,  Hydraulic  Ce- 
ments, and  Mortars.  Paper  >  on  Practical  Engineering,  U. 
S.  En;r:B.  er  Department,  No.  9,  containing  Reports,  of 
numerous  Experiments  conducted  in  New  York  City  during 
the  years  i85i>  to  1861,  inclusive.  With  nuirerous  illustra- 
tions. 8vo,  cloth 4  oo 

Practical  Treatise  on  the  Construction  of  Roads,  Streets, 

and  Pavements.     With  70  illustrations.     I2mo,  cloth 2  oo 

Report  on  Strength  of  the  Building  Stones  in  the  United 

States,  etc.    8vo,  illustrated,  cloth      150 

Coignet  Beton  and  other  Artificial  Stone.    9  plates,  views, 

etc .    8vo,  clot  h 2  50 

GOODEVE  (T.  M.)    A  Text-Book  on  the  Steam-Engine.     143 

illustrations.     I2mo,  cloth 2  oo 

GORDON  (J.  E.  H.)   Four  Lectures  on  Static  Induction.    lamo, 

cloth.... 80 


6  D.  VAN  NOSTRATSD'S  PUBLICATIONS. 

GRUNER  (M.  L.)  The  Manufacture  of  Steel.  Translated 
from  the  French,  by  Lenox  Smith,  with  an  appendix  on  the 
Bessemer  process  in  the  United  States,  by  the  translator. 
Illustrated,  8vo,  cloth $35° 

HALF-HOURS  WITH  MODERN  SCIENTISTS.  Lectures 
and  Essays.  By  Professors  Huxley,  Barker,  Stirling,  Cope, 
Tyndall,  Wallace,  Rpscoe,  Huggins,  Lockyer,  Young, 
Mayer,  and  Reed.  Being  the  University  Series  bound  up. 
With  a  general  introduction  by  Noah  Porter,  President  of 
Yale  College.  •  2  vols.  izmo,  cloth,  illustrated 2  50 

HAMILTON  (W.  G.)  Useful  Information  for  Railway  Men. 
Sixth  edition,  revised  and  enlarged.  562  pages,  pocket  form. 
Morocco,  gilt . .... 200 

HARRISON  (W.  B.)  The  Mechanic's  Tool  Book^  with  Prac- 
tical Rules  and  Suggestions  for  Use  of  Machinists,  Iron- 
Workers,  and  others.  Illustrated  with  44  engravings. 
I2mo,  cloth I  50 

HASKINS  (C.  H.)  The  Galvanometer  and  its  Uses.  A  Man- 
ual for  Electricians  and  Students.  Second  edition.  I2mo, 
morocco I  5° 

HENRICI  (OLAUS).  Skeleton  Structures,  especially  in  their 
application  to  the  Building  of  Steel  and  Iron  Bridges.  With 
folding  plates  and  diagrams.  8vo,  cloth I  50 

HEWSON  (WM.)  Principles  and  Practice  of  Embanking 
Lands  from  River  Floods,  as  applied  to  the  Levees  of  the 
Mississippi.  8vo,  cloth ^. . .  2  oo 

HOLLEY  (ALEX.  L.)  A  Treatise  on  Ordnance  and  Armor,  em- 
bracing descriptions,  discussions,  and  professional  opinions 
concerning  the  materials,  fabrication,  requirements,  capa- 
bilitie«,  and  endurance  of  European  and  American  Guns, 
for  Naval,  Sea-Coast,  and  Iron-Clad  Warfare,  and  their 
Rifling,  Projectiles,  and  Breech-Loading ;  also,  results  of 
experiments  against  armor,  from  official  records,  with  an 
appendix  referring  to  Gun-Cotton,  Hooped  Guns,  etc.,  etc. 
948  pages,  403  engravings,  and  147  Tables  of  Results,  etc. 
8vo,  half  roan 10  oo 

Railway  Practice.  American  and  European  Railway 

Practice  in  the  economical  Generation  of  Steam,  including 
the  Materials  and  Construction  of  Coal-burning  Boilers, 
Combustion,  the  Variable  Blast,  Vaporization,  Circulation, 
Superheating,  Supplying  and  Heating  Feed-water?  etc., 
and  the  Adaptation  of  Wood  and  Coke-burning  Engines  to 
Coal-burning  ;  and  in  Permanent  Way,  including  Road-bed, 
Sleepers,  Rails,  Joint-fastenings,  Street  Railways,  etc.,  etc. 
With  77  lithographed  plates.  Folio,  cloth 12  oo 

HOWARD  (C.  R.)  Earthwork  Mensuration  on  the  Basis  of 
the  Prismoidal  Formulas.  Containing  simple  and  labor- 
saving  method  of  obtaining  Prismoidal  Contents  directly 


D.    VAN  NOSTBAND  S  PUBLICATIONS.  7 

from  End  Areas.  Illustrated  by  Examples,  and  accom- 
panied by  Plain  Rules  for  Practical  Uses.  Illustrated.  8vo, 
cloth  $l  50 

INDUCTION-COILS.  How  Made  and  How  Used.  63  illus- 
trations. i6mo,  boards  50 

ISHERWOOD  (B.  F.)  Engineering  Precedents  for  Steam  Ma- 
chinery. Arranged  in  the  most  practical  and  useful  manner 
for  Engineers.  With  illustrations.  Two  volumes  in  one. 
8vo,  cloth 250 

JANNETTAZ  (EDWARD).  A  Guide  to  the  Determination  of 
Rocks:  being  an  Introduction  to  Lithology  Translated 
from  the  French  by  G.  W.  Plympton,  Professor  of  Physical 
Science  at  Brooklyn  Polytechnic  Institute.  i2mo,  cloth....  i  50 

JEFFERS  (Capt.  W.  N.,  U.  S.  N.)  Nautical  Surveying.  Illus- 
trated with  9  copperplates  and  31  wood-cut  illustrations. 
8vo,  cloth 500 

JONES  (H.  CHAPMAN).  Text-Book  of  Experimental  Or- 
ganic Chemistry  for  Students.  i8mo,  cloth  . .  x  oo 

JOYNSON  (F.  H.)  The  Metals  used  in  Construction:  Iron, 

Steel,  Bessemer  Metal,  etc.,  etc.  Illustrated.  i2mo,  cloth.  75 

Designing  and  Construction  of  Machine  Gearing.  Illus- 
trated. 8vo,  cloth 200 

KANSAS  CITY  BRIDGE  (THE).  With  an  account  of  the 
Regimen  of  the  Missouri  River,  and  a  description  of  the 
methods  used  for  Founding  in  that  River.  By  O.  Chanute, 
Chief-Engineer,  and  George  Morrison,  Assistant-Engineer. 
Illustrated  with  five  lithographic  views  and  twelve  plates  of 
plans.  410,  cloth 6  oo 

KING  (W.  H.)  Lessons  and  Practical  Notes  on  Steam,  the 
Steam-Engine,  Propellers,  etc.,  etc  ,  for  young  Marine  En- 
gineers, Students,  and  others.  Revised  by  Chief-Engineer 
J.  W.  King,  U.  S.  Navy.  Nineteenth  edition,  enlarged. 
8vo,  cloth 2  oo 

KIRKWOOD  (JAS.  P.)  Report  on  the  Filtration  of  River 
Waters  for  the  supply  of  Cities,  as  practised  in  Europe, 
made  to  the  Hoard  of  Water  Commissioners  of  the  City  of 
St.  Louis.  Illustrated  by  30  double-plate  engravings.  410,. 
cloth .  .15  o» 

LARRAREE  (C.  S.)  Cipher  and  Secret  Letter  and  Telegra- 
phic Code,  with  Hogg's  Improvements.  The  most  perfect 
secret  code  ever  invented  or  discovered.  Impossible  to  read 
without  the  key.  i8mo,  cloth X  oo 

LOCK  (C.  G.),  WIGNER  (G.  W.),  and  HARLAND  (R.  H.) 
Sugar  Growing  and  Refining.  Treatise  on  the  Culture  of 
Sugar-Yielding  Plants,  and  the  Manufacture  and  Refining  of 
Cane,  Beet,  and  other  sugars.  8vo,  cloth,  illustrated 12  00 


'8  D.  VAN  NOSTRAND'S  PUBLICATIONS. 

LOCKWOOD  (THOS.  D.)  Electricity.  Magnetism,  and  Elec- 
tro-Telegraphy. A  Practical  Guide  lor  Students,  Operators, 
and  Inspectors.  8vo,  cloth ...$250 

:LORING  (A.  E.)  A  Hand-Book  on  the  Electro-Magnetic  Tele- 
graph. Paper  boards o  50 

Cloth . 75 

Morocco I  oo 

.MACCORD  (Prof.  C.  W )  A  Practical  Treatise  on  the  Slide- 
Valve  by  Eccentrics,  examining  by  methods  the  action  of 
the  Eccentric  upon  the  Slide-Valve,  and  explaining  the  prac- 
tical processes  of  laying  out  the  movements,  adapting  the 
valve  for  its  various  duties  in  the  steam-engine.  Second  edi- 
tion. Illustrated.  4to,  cloth 2  50 

McCULLOCH  (Prof.  R.  S.)  Elementary  Treatise  on  the  Me- 
chanical Theory  of  Heat,  and  its  application  to  Air  and 
Steam  Engines.  8vo,  cloth 3  5° 

.MERRILL  (Col.  WM.  E.,  U.  S.  A.)  Iron  Truss  Bridges  for 
Railroads.  The  method  of  calculating  strains  in  Trusses, 
with  a  careful  comparison  of  the  most  prominent  Trusses,  in 
reference  to  economy  in  combination,  etc.,  etc.  Illustrated. 
4to,  cloth 5  oo 

MICHAELIS  (Capt.  O.  E.,  U.  S.  A.)  The  Le  Boulenge 
Chronograph,  with  three  lithograph  folding  plates  of  illus- 
trations. 410,  cloth 300 

MICHIE  (Prof.  P.  S.)  Elements  of  Wave  Motion  relating  to 
Sound  and  Light.  Text-Book  forthe  U.S.  Military  Acade- 
my. 8vo,  cloth,  illustrated 5  °° 

MINIFIE  (WM.)  Mechanical  Drawing.  A  Text-Book  of  Geo- 
metrical Drawing  for  the  use  of  Mechanics  and  Schools,  in 
which  the  Definitions  and  Rules  of  Geometry  are  familiarly 
explained  ;  the  Practical  Problems  are  arranged,  from  the 
most  simple  to  the  more  complex,  and  in  their  description 
technicalities  are  avoided  as  much  as  possible.  With  illus- 
trations for  Drawing  Plans,  Sections,  and  Elevations  of 
Railways  and  Machinery:  an  Introduction  to  Isometrical 
Drawing,  and  an  Essay  on  Linear  Perspective  and  Shadows. 
Illustrated  with  over  200  diagrams  engraved  on  steel.  Ninth 
edition.  With  an  Appendix  on  the  Theory  and  Application 

of  Colors.    8vo,  cloth  4  oo 

"It  is  the  best  work  on  Drawing  that  we  have  ever  seen,  and  is 
especially  a  text-book  of  Geometrical  Drawing  for  the  use  of  Me- 
chanics and  Schools.  No  young  Mechanic,  such  as  a  Machinist, 
Engineer,  Cabinet-maker,  Millwright,  or  Carpenter,  should  be  with- 
out it." — Scientific  American. 

.            Geometrical  Drawing.     Abrideed  from  the  octavo  edi- 
•%  tion,  for  the  use  of  schools.    Illustrated  with  forty-eight 
steel  plates.    Fifth  edition.    i2mo,  cloth 2  oo 


D.  VAN  NOSTRAND'S  PUBLICATIONS.  9 

MODERN  METEOROLOGY.  A  Series  of  Six  Lectures,  de- 
livered under  the  auspices  of  the  Meteorological  Society 
in  1878.  Illustrated,  izmo,  cloth $l  50 

MORRIS  (E.)  Easy  Rules  for  the  Measurement  of  Earth- 
works, by  Means  of  the  Prismoidal  Formula.  78  illustra- 
tions. 8vo,  cloth I  50 

MOTT  (H.  A  ,  Jr.)  A  Practical  Treatise  on  Chemistry  (Quali- 
tative and  Quantitative  Analysis),  Stoichiometry,  Blow-pipe 
Analysis,  Mineralogy,  Assaying.  Pharmaceutical  Prepara- 
tions, Human  Secretions,  Specific  Gravities,  Weights  and 
Measures,  etc.,  etc.,  etc.  New  edition,  1883.  650  pages. 
8vo,  cloth 4  00 

NAQUET  (A.)  Legal  Chemistry.  A  Guide  to  the  Detection  of 
Poisons,  Falsification  of  Writings,  Adulteration  of  Alimen- 
tary and  Pharmaceutical  Substances,  Analysis  ^of  Ashes, 
and  examination  of  Hair.  Coins,  Arms,  and  Stains,  as  ap- 


2mo,  cloth 2  oo 


NOBLE  (W.  H.)    Useful  Tables.    Pocket  form,  cloth 50 

NUGENT  (E.)  Treatise  on  Optics ;  or,  Light  and  Sight,  theo- 
retically and  practically  treated,  with  the  application  to 
Fine  Art  and  Industrial  Pursuits.  With  103  illustrations. 
I2mo,  cloth i  50 

PEIRCE  (B.)    System  of  Analytic  Mechanics.    410,  cloth to  oo 


PLANE  TABLE  'THE).  Its  Uses  in  Topographical  Survey- 
ing. From  the  Papers  of  the  U.  S.  Coast  Survey.  Illustrat- 
ed. 8vo,  cloth 2  oo 

"  This  work  gives  a  description  of  the  Plane  Table  employed  at 

the  U.  S.  Coast  Survey  office,  and  the  manner  of  using  it." 

PLATTNER.  Manual  of  Qualitative  and  Quantitative  An- 
alysis with  the  Blow-Pipe.  From  the  last  German  edition, 
revised  and  enlarged.  By  Prof.  Th.  Richter,  of  the  Royal 
Saxon  Mining  Academy.  Translated  by  Prof.  H.  B.  Corn- 
wall, assisted  by  John  H.Caswell.  Illustrated  with  87  wood- 
cuts and  one  lithographic  plate.  Fourth  edition,  revised, 
560  pages.  8vo,  cloth 5  oo 

PLYMPTON  (Prof.  GEO.  W.)  The  Blow-Pipe.  A  Guide  to  its 
use  in  the  Determination  of  Salts  and  Minerals.  Compiled 
from  various  sources.  I2mo,  cloth I  50 

The  Aneroid  Barometer:    Its  Construction  and  Use. 

Compiled  from  several  sources.    i6mo,  boards,  illustrated,      50 
Morocco , 100 


10          D.  VAN  NOSTRAND'S  PUBLICATIONS. 

PLYMPTON  (Prof.  GEO.  W.)  The  Star-Finder,  or  Plani- 
sphere, with  Movable  Horizon.  Printed  in  colors  on  fine 
card-board,  and  in  accordance  with  Proctor's  Star  Atlas.  ..$100 

POCKET  LOGARITHMS,  to  Four  Places  of  Decimals,  includ- 
ing Logarithms  of  Numbers,  and  Logarithmic  Sines  and 
Tangents  to  Single  Minutes.    To  which  is  added  a  Table  of 
Natural  Sines,  Tangents,  and  Co-Tangents.      i6mo,  boards,      50 
Morocco i  oo 

POOK  (S.  M.)  Method  of  Comparing  the  Lines  and  Draught- 
ing Vessels  propelled  by  Sail  or  Steam.  Including  a  chap- 
ter on  Laying-offon  the  Mould-Loft  Floor,  i  vol.  Svo,  with 
illustrations,  cloth S  °° 

POPE  (F.  L.)  Modern  Practice  of  the  Electric  Telegraph.  A 
Hand-Book  for  Electricians  and  Operators.  Eleventh  edi- 
tion, revised  and  enlarged,  and  fully  illustrated.  Svo,  cloth.  2  oo 

PRESCOTT  (Prof.  A.  B.)  Outlines  of  Proximate  Organic  An- 
alysis, for  the  Identification,  Separation,  and  Quantitative 
Determination  of  the  more  commonly  occurring  Organic 
Compounds.  I2mo,  cloth i  75 

Chemical  Examination  of  Alcoholic  Liquors.  A  Manual 

of  the  Constituents  of  the  Distilled  Spirits  and  Fermented 
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RICE  (Prof.  J.  M.)  and  JOHNSON  (Prof.  W.  W.)  On  a  New 
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SAWYER  (W.  E.)  Electric-Lighting  by  Incandescence,  and 
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SCRIBNER  (J.  M.)  Enginee»s'  and  Mechanics'  Companion, 
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THE    UNIVERSITY  SERIES. 

No.  i.  ON  THE  PHYSICAL  BASIS  OF  LIFE.  By  Prof.  T.  H. 
Huxley,  LL.D.,  F.R.S.  With  an  introduction  by  a  Professor 
in  Yale  College.  I2mo,  pp.  36.  Paper  cover 25 

No.  2.  THE  CORRELATION  OF  VITAL  AND  PHYSICAL 
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lege. 36  pp.  Paper  covers 25 

No.  3.  AS  REGARDS  PROTOPLASM,  in  relation  to  Prof.  Hux- 
ley's "Physical  Basis  of  Life."  By  J.  Hutchinson  Stirling, 
F.R.C.S.  72  pp 25 

No.  4.  ON  THE  HYPOTHESIS  OF  EVOLUTION,  Physical 
and  Metaphysical.  By  Prof.  Edward  D.  Cope.  I2mo,  72  pp. 
Paper  covers 25 

No.  5.  SCIENTIFIC  ADDRESSES-i.  On  the  Methods  and 
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Dust.  3.  On  the  Scientific  Use  of  the  Imagination.  By 

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No.  6.  NATURAL  SELECTION  AS  APPLIED  TO  MAN.  By 
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(2)  tne  Limits  of  Natural  Selection  as  applied  to  Man.  54  pp.  25 

No.7.  SPECTRUM  ANALYSIS.  Three  lectures  by  Profs. 
Roscoe,  Huggins,  and  Lockyer.  Finely  illustrated.  88  pp. 
Paper  covers 25 

No.  8.  THE  SUN.  A  sketch  of  the  present  state  of  scientific 
opinion  as  regards  this  body.  By  Prof.  C.  A.  Young,  Ph.D., 
of  Dartmouth  College.  58  pp.  Paper  covers 25 


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No.  10.  MYSTERIES  OF  THE  VOICE  AND  EAR.  By  Prof. 
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Ortogether,  2vols., cloth ,  $2  50 


D.  VAN  NOSTRAND'S  PUBLICATIONS. 


VAN  NOSTRAND'S  SCIENCE  SERIES. 

(i8mo,    green    boards.      Amply    illustrated    where    the    subject 
demands.) 

No.  I.  CHIMNEYS  FOR  FURNACES,  FIRE-PLACES,  AND 
STEAM-BOILERS.  By  R.  Armstrong,  C.E.  Second  edi- 
tion, enlarged 50 

No.  2.  STEAM-BOILER  EXPLOSIONS.     By  Zerah  Colburn. .  50 

No.  3.  PRACTICAL  DESIGNING  OF  RETAINING  WALLS. 
By  Arthur  Jacob,  A.B 50 

No  4.  PROPORTIONS  OF  PINS  USED  IN  BRIDGES.  By 
Charles  Bender,  C.E 50 

No.  5.  VENTILATION  OF  BUILDINGS.    By  W.  F.  Butler. . .  50 

No.  6.  ON  THE  DESIGNING  AND  CONSTRUCTION  OF 
STORAGE  RESERVOIRS.  By  Arthur  Jacob,  A. B 50 

No.  7.  SURCHARGED  AND  DIFFERENT  FORMS  OF  RE- 
TAINING WALLS.  By  James  S.  Tate,  C.E 50 

No.  8.  A  TREATISE  ON  THE  COMPOUND  ENGINE.  By 
Tohn  Turnbull,  Jr.  Second  edition,  revised  by  Prof.  S.  W. 
*  >binson 50 

No.  g.  FUEL.  By  C.  William  Siemens,  D.C.L.;  to  which  is  ap- 
pended the  VALUE  OF  ARTIFICIAL  FUEL  AS  COM- 
PARED WITH  COAL.  By  John  Wormald,  C.E y> 

No.  10.  COMPOUND  ENGINES.  Translated  from  the  French 
of  A.  Mallet 50 

No.  ii.  THEORY  OF  ARCHES.    By  Prof.  W.  Allan 50 

No.  12.  A  THEORY  OF  VOUSSOIR  ARCHES.  By  Prof.  W. 
E.Cain 5° 

No.  13.  GASES  MET  WITH  IN  COAL-MINES.  By  J.  J.  At- 
kinson    $o 

No.  14.  FRICTION  OF  AIR  IN  MINES.    By  J.  J.  Atkinson  ...  50 

No.  is-  SKEW  ARCHES.  By  Prof.  E.  W.  Hyde,  C.E.  Illus- 
trated  50 

No.  16.  A  GRAPHIC  METHOD  FOR  SOLVING  CERTAIN 
ALGEBRAIC  EQUATIONS.  By  Prof.  George  L.  Vose. . .  50 

No.  17.  WATER  AND  WATER  SUPPLY.  By  Prof.  W.  H. 
Corfield,  of  the  University  College,  London 50 

No.  18.  SEWERAGE  AND  SEWAGE  UTILIZATION.  By 
Prof.  W.  H. Corfield,  M.A.,  of  the  University  College,  Lon- 
don  50 

No.  IQ.  STRENGTH  OF  BEAMS  UNDER  TRANSVERSE 
LOADS.  By  Prof.  W.  Allan,  author  of  "  Theory-of  Arches  "  50 


'johi 
Rob 


D.  VAN  NOSTRAND'S  PUBLICATIONS. 

No.  20.  BRIDGE  AND  TUNNEL  CENTRES.    By  John  B.  Mc- 

Master,  C.E 50 

No.  21.  SAFETY  VALVES.     By  Richard  H.  Buel,C.E ,...  50 

No.  22.  HIGH  MASONRY  DAMS.  By  John  B.  McMaster, 
C.E .'50 

No.  23.  THE  FATIGUE  OF  METALS  UNDER  REPEATED 
STRAINS,  with  Various  Tables  of  Results  and  Experiments. 
From  the  German  of  Prof.  Ludwig  Spamgenburgh,  with  a 
PrefacebyS.  H.  Shreve,  A.M . ...! 50 

No.  24.  A  PRACTICAL  TREATISE  ON  THE  TEETH  OF 
WHEELS.  Bv  Prof.  S.  W.  Robinson 50 

No.  25.  ON  THE  THEORY  AND  CALCULATION  OF  CON- 
TINUOUS  BRIDGES.  By  Mansfield  Merriman,  Ph.D 50 

No.  26.  PRACTICAL  TREATISE  ON  THE  PROPERTIES 
OF  CONTINUOUS  BRIDGES.  By  Charles  Bender.  C.E.  50 

No.  27.  ON  BOILER  INCRUSTATION  AND  CORROSION. 
ByF.J.  Rowan 50 

No.  28.  TRANSMISSION  OF  POWER  BY  WIRE  ROPES. 
By  Albert  W.  Stahl,  U.  S.  N 50 

No.  20.  STEAM  INJECTORS.  Translated  from  the  French  of 
M.  Leon  Pochet 50 

No.  30.  TERRESTRIAL  MAGNETISM  AND  THE  MAG- 
NETISM OF  IRON  VESSELS.  By  Prof.  Fairman  Ro- 
gers  50 

No.  31.  THE  SANITARY  CONDITION  OF  DWELLING- 
HOUSES  IN  TOWN  AND  COUNTRY.  By  George  E. 
Waring,  Jr 50 

No.  32.  CABLE-MAKING  OF  SUSPENSION  BRIDGES.  By 
W.  Hildenbrand,  C.E .50 

No.  33.  MECHANICS  OF  VENTILATION.  By  George  W. 
Rafter,  C  E .  . . . 50 

No.  34.  FOUNDATIONS.  By  Prof.  Jules  Gaudard,  C.E.  Trans- 
lated from  the  French. 50 

No.  35.  THE  ANEROID  BAROMETER:  ITS  CONSTRUC- 
TION AND  USE.  Compiled  by  George  W.  Plympton. 
Second  edition 50 

No.  36.  MATTER  AND  MOTION.    By  J.  Clerk  Maxwell,  M. A.  50 

No.  37.  GEOGRAPHICAL  SURVEYING :  Its  Uses,  Meth- 
ods, and  Results.  By  Frank  De  Yeaux  Carpenter,  C  E.  50 

No.  38.  MAXIMUM  STRESSES  IN  FRAMED  BRIDGES. 
By  Prof.  Wm.  Cain,  A.M.,  C.E 50 

No.  39.  A  HAND-BOOK  OF  THE  ELECTRO-MAGNETIC 
TELEGRAPH.  By  A.  E.  Loring 50 

No.  40.  TRANSMISSION  OF  POWER  BY  COMPRESSED 
AIR.  By  Robert  Zahner,  M.E 50 

No.  41.  STRENGTH  OF  MATERIALS.    By  Wm.  Kent,  C.E..  50 


D.  VAN  NOSTRAND'S  PUBLICATIONS. 

No. 42.  VOUSSOIR  ARCHES  APPLIED  TO  STONE 
BRIDGES,  TUNNELS,  CULVERTS,  AND  DOMES.  By 

Prof.  Wm.  Cain 50 

No.  43.  WAVE  AND  VORTEX  MOTION.  By  Dr.  Thomas 
Craig,  of  Johns  Hopkins  University 50 

No.  44.  TURBINE  WHEELS.  By.  Prof.  W.  P.  Trowbridge, 
Columbia  College  50 

No  45.  THERMODYNAMICS.  By  Prof.  H.  T.  Eddy,  Univer- 
sity of  Cincinnati  50 

No.  46.  ICE-MAKING  MACHINES.  From  the  French  of  M. 
Le  Doux 50 

No.  47.  LINKAGES;  THE  DIFFERENT  FORMS  AND 
UbES  OF  ARTICULATED  LINKS.  By  J.  D.  C.  De 
Roos  ...  50 

No.  48.  THEORY  OF  SOLID  AND  BRACED  ARCHES.  By 
Wm.  Cain,  C.E 50 

No.  49.  ON  THE  MOTION  OF  A  SOLID  IN  A  FLUID. 
By  Thomas  Craig,  Ph. D 50 

No.  50  DWELLING  HOUSES:  Their  Sanitary  Construction 
and  Arrangements.  By  Prof.  W.  H.  Corfield 50 

No.  51.  THE  TELESCOPE  :  Its  Construction,  etc.  By  Thos. 
Nolan 50 

No.  52  IMAGINARY  QUANTITIES.  Translated  from  the 
French  of  M.  Argann.  By  Prof.  Hardy 50 

N  ,.  53.  INDUCTION  COILS:    How  Made  and  How  Used....  50 

No.  54.  KINEMATICS  OF  MACHINERY.  By  Prof.  Kennedy. 
With  an  introduction  by  Prof.  R.  H.  Thurston 50 

No.  55.  SEWER  GASES  :  Their  Nature  and  Origin.  By  A.  De 
Varona 50 

No.  *6.  THE  ACTUAL  LATERAL  PRESSURE  OF  EARTH- 
WORK. By  Benj.  Baker,  M.  Inst.  C.E 50 

No.  57.  INCANDESCENT  ELECTRIC  LIGHTS,  WITH  PAR- 
TICULAR REFERENCE  TO  THE  EDISON  LAMPS  AT 
THE  PARIS  EXHIBITION.  By  Comte  Th.  Du  Moncel, 
Wm.  Henry  Preece,  J.  W.  Howell,  and  others.  Second  edi- 
tion.   50 

No.  *8.  THE  VENTILATION  OF  COAL-MINES.  By  W. 
Fairley,  M.E.,  F.S.S 50 

No.  59.  RAILROAD  ECONOMICS  ;  or,  Notes,  with  Com- 
ments. By  S.  W.  Robinson,  C.E 50 

No.  60.  STRENGTH  OF  WROUGHT-IRON  BRIDGE  MEM- 
BERS. By  S.  W.  Robinson,  CE 50 

No.  61.  POTABLE  WATER  AND  THE  DIFFERENT 
METHODS  OF  DETECTING  IMPURITIES.  By  Chas. 
W.  Folkard.  50 


D.  TAN  NOSTRAND'S  PUBLICATIONS. 

No.  62.  THE  THEORY  OF  THE  GAS  ENGINE.  ByDugald 
Clerk 50 

No.  63.  HOUSE  DRAINAGE  AND  SANITARY  PLUMB- 
ING. By  W.  P.  Gerhard So 

No.  64.  ELECTRO-MAGNETS.    By  Th.  Du  Moncel so 

No.  65.  POCKET  LOGARITHMS  TO  FOUR  PLACES  DE- 
CIMALS    50 

No.  66.  DYNAMO-ELECTRIC  MACHINERY.  By  S.  P. 
Thompson.  With  notes  by  F.  L.  Pope 50 

No.  67.  HYDRAULIC  TABLES,  BASED  ON  "  KUTTER'S 
FORMULA."  ByP.J.Flynn 50 

No.  68.  STEAM-HEATING.    By  Robert  Briggs 50 

No.  69.  CHEMICAL  PROBLEMS.  By  Prof.  J.  C.  Foyc.  Sec- 
ond edition,  revised  and  enlarged  50 

No.  70.  EXPLOSIVES  AND  EXPLOSIVE  COMPOUNDS. 
By  M.  Bertholet,., 50 

No.  71.  DYNAMIC  ELECTRICITY.  By  John  Hopkinson,  J. 
A,  Schoolbred,  and  R.  E.  Day  , 50 


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